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14 pages, 731 KiB  
Article
Quantum Congestion Game for Overcrowding Prevention Within Airport Common Areas
by Evangelos D. Spyrou, Vassilios Kappatos and Chrysostomos Stylios
Computers 2024, 13(11), 298; https://doi.org/10.3390/computers13110298 - 17 Nov 2024
Viewed by 507
Abstract
Quantum game theory merges principles from quantum mechanics with game theory, exploring how quantum phenomena such as superposition and entanglement can influence strategic decision making. It offers a novel approach to analyzing and optimizing complex systems where traditional game theory may fall short. [...] Read more.
Quantum game theory merges principles from quantum mechanics with game theory, exploring how quantum phenomena such as superposition and entanglement can influence strategic decision making. It offers a novel approach to analyzing and optimizing complex systems where traditional game theory may fall short. Congestion of passengers, if considered as a network, may fall into the categories of optimization cases of quantum games. This paper explores the application of quantum potential games to minimize congestion in common areas at airports. The players/passengers of the airport have identical interests and they share the same utility function. A metric is introduced that considers a passenger’s visit to a common area by setting their preferences, in order to avoid congestion. Passengers can decide whether to visit a specific common area or choose an alternative. This study demonstrates that the proposed game is a quantum potential game for tackling congestion, with identical interests, ensuring the existence of a Nash equilibrium. We consider passengers to be players that want to ensure their interests. Quantum entanglement is utilized to validate the concept, and the results highlight the effectiveness of this approach. The objective is to ensure that not all passengers select the same common place of the airport to reduce getting crowded; hence, the airborne disease infection probability increases due to overcrowding. Our findings provide a promising framework for optimizing passenger flow and reducing congestion in airport common areas through quantum game theory. We showed that the proposed system is stable by encapsulating the Lyapunov stability. We compared it to a simulated annealing approach to show the efficacy of the quantum game approach. We acknowledge that this framework can be utilized in other disciplines as well. For our future work, we will research different strategies than binary ones to investigate the efficacy of the approach. Full article
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<p>Value of the potential function: non-smooth.</p>
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<p>Value of the potential function: smooth.</p>
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<p>Value of the potential function: simulated annealing.</p>
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<p>Evolution of strategies: utility based.</p>
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<p>Evolution of strategies: SA.</p>
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17 pages, 1265 KiB  
Article
Message Action Adapter Framework in Multi-Agent Reinforcement Learning
by Bumjin Park and Jaesik Choi
Appl. Sci. 2024, 14(21), 10079; https://doi.org/10.3390/app142110079 - 4 Nov 2024
Viewed by 824
Abstract
Multi-agent reinforcement learning (MARL) has demonstrated significant potential in enabling cooperative agents. The communication protocol, which is responsible for message exchange between agents, is crucial in cooperation. However, communicative MARL systems still face challenges due to the noisy messages in complex multi-agent decision [...] Read more.
Multi-agent reinforcement learning (MARL) has demonstrated significant potential in enabling cooperative agents. The communication protocol, which is responsible for message exchange between agents, is crucial in cooperation. However, communicative MARL systems still face challenges due to the noisy messages in complex multi-agent decision processes. This issue often stems from the entangled representation of observations and messages in policy networks. To address this, we propose the Message Action Adapter Framework (MAAF), which first trains individual agents without message inputs and then adapts a residual action based on message components. This separation isolates the effect of messages on action inference. We explore how training the MAAF framework with model-agnostic message types and varying optimization strategies influences adaptation performance. The experimental results indicate that MAAF achieves competitive performance across multiple baselines despite utilizing only half of the available communication, and shows an average improvement of 7.6% over the full attention-based communication approach. Additional findings suggest that different message types result in significant performance variations, emphasizing the importance of environment-specific message types. We demonstrate how the proposed architecture separates communication channels, effectively isolating message contributions. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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<p>Graphical illustration of two types of actions. The observation action is a non-cooperative behavior in which the prey can easily escape the predators. On the other hand, the messages encourage better cooperative behavior. The messages contribute to residuals of actions; the final actions combine the base actions and the residuals.</p>
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<p>Graphical models for the forward action process in policy networks. Previous MARL methods link hidden representations to an intermediate hidden layer (Hidden2), resulting in entangled representations. In contrast, the proposed action adaptation restricts the contribution of messages to the action logit, offering a more disentangled integration. The interaction between observation and messages can be constructed by passing observation to the message (dashed line).</p>
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<p>Graphical illustration of MAAF. (<b>Left</b>) Two steps for training: a base policy and a message adapter policy (blue and orange regions). In step 1, the agent learns to maximize the environment return without communication. In step 2, the agent generates messages and communicates with cooperative agents. The adapter policy produces a residual action <math display="inline"><semantics> <msup> <mi>A</mi> <mo>′</mo> </msup> </semantics></math> resulting in the final action <math display="inline"><semantics> <mover accent="true"> <mi>A</mi> <mo>˜</mo> </mover> </semantics></math>. In the training of the adapter policy, the parameters of the base policy are fixed. (<b>Right</b>) Overview of MARL control for two steps. Each agent produces action and communicates by generating messages.</p>
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<p>Graphical illustration of message generation. The combination of four types generates message <span class="html-italic">M</span> for cooperative agents. Optionally, a user can feed a new message input type to utilize communication.</p>
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<p>Rendering of three environments. In the spread environment, three agents (purple circles) must spread as far as possible while staying near target locations (small black circles). In the tag environments, three predators (red circles) chase prey (a green circle) in an environment with obstacles. In SMAC environments, two groups of agents fight each other.</p>
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<p>Episode returns for three optimizations (Y-axis) for 2M time steps (X-axis). Adaptations are started at the 1M time step. The results indicate that updating both policies (red) is better than freezing blue). The shaded regions are confidence intervals obtained by three random seeds.</p>
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<p>Episode returns for message types. The solid lines are the cases when updating base and adaptation policies, and the dashed lines are cases when the base policies are not updated. Each color represents different message types in <math display="inline"><semantics> <msub> <mi mathvariant="script">S</mi> <mo form="prefix">Comb</mo> </msub> </semantics></math>. When freezing, the performance drops after the 1M time step, indicating that updating both networks is robust for message types.</p>
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<p>Episodic return while training five MARL agents for the best hyperparameter settings and three random seeds. We observe the competitive performance of MAPPO for all environments. In the tag environment, where communication between agents is crucial to tracking moving agents, the proposed MAAF variants perform better than all the baselines. However, MAAF shows weak results in SMAC environments where the number of actions is too large to be adapted. Therefore, MAAF shows a large gap to MAPPO in SMAC.8M, which has eight agents.</p>
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<p>Box plots of normalized returns for different environments. Each plot is obtained by running three seeds. In a spread environment, we observed no difference between message types, indicating that the contribution of messages is weak. In the tag environment, the performance increases as communication message types become complex. In SMAC environments, simple messages, such as only having observation or action, provide better performance than having complex message types. These results indicate that feature selection on message types is necessary for MARL communication.</p>
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<p>Box plots of returns of tag environments for different numbers of predators (the number in the naming represents the number of predators). Each plot is obtained by running three seeds. In Tag-2, the performance drops as the communication channel includes more message types. In Tag-3, the performance increases as the complexity of the communication channel increases. The action information is especially beneficial, and the best performance is obtained with both action and probability. This correlation between the complexity of message channels and environments no longer holds in Tag-4. Therefore, searching for the optimal combination might be necessary.</p>
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<p>Trajectories for the base and adapted policies (with message cases) in the spread environment. Black and blue stars are the locations of three agents with and without communication, respectively. The darker color represents later time steps. Diamond is the target location where three agents (represented by stars) must be close to obtain rewards while separating each other.</p>
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<p>Counterfactual interpretation of actions following the trajectory of a base policy. Each panel shows the trajectories of an episode in the Tag environment, featuring two predators and one prey. The trajectories are represented by stars, with darker colors indicating later time steps. Green arrows represent the prey’s actions, while red arrows show the actions of the predators. The gray arrows denote counterfactual actions generated through communication between predators. This setup allows us to interpret actions without communication and compare them to cooperative actions facilitated by communication.</p>
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<p>Pseudo-code for computing action logits in two configurations: (1) Base Actor, which computes logits solely from observations, and (2) Adapter Actor, which incorporates both observations and messages. In the Adapter Actor computation, logits from the base and adapter networks are linearly combined to produce the final action logits.</p>
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9 pages, 416 KiB  
Article
Is Canada Moving towards a More Agile Regulatory Approval and Reimbursement Process with a Shifting Role for Real-World Evidence (RWE) for Oncology Drugs?
by Catherine Y. Lau and Nigel S. B. Rawson
Curr. Oncol. 2024, 31(9), 5599-5607; https://doi.org/10.3390/curroncol31090414 - 18 Sep 2024
Viewed by 1387
Abstract
Canada is known to have a complex pathway for new drug approval and reimbursement, resulting in delayed access for patients with serious and life-threatening diseases, such as cancer. Several recent publications from key stakeholders, including patients, physicians and policymakers, highlight patient helplessness, physician [...] Read more.
Canada is known to have a complex pathway for new drug approval and reimbursement, resulting in delayed access for patients with serious and life-threatening diseases, such as cancer. Several recent publications from key stakeholders, including patients, physicians and policymakers, highlight patient helplessness, physician frustrations and policymakers entangled in a massive network of bureaucracy unable to make headway. Several quantitative and qualitative assessments using time from regulatory approvals to successful reimbursements confirm long review times and high rejection rates for oncology drugs, especially those receiving conditional approvals. A consensus forum of 18 Canadian oncology clinicians recently voiced frustration with the process and inability to deliver guideline-supported efficacious therapies to their patients. This manuscript compares data extracted from publicly available data sources from 2019 to June 2024 to previous publications. Methods: Public databases from Health Canada, the Canadian Agency for Drugs and Technologies in Health (CADTH), which is in the process of changing to Canada’s Drug Agency, and the pan-Canadian Pharmaceutical Alliance (pCPA) were reviewed and the data collected were analyzed with descriptive statistics. Results: From the data, three trends emerge, (i) an increasing number of oncology drugs are receiving conditional approvals from Health Canada, (ii) the percentage of conditionally approved oncology drugs receiving positive reimbursement recommendations from CADTH is still low but appears to be improving, but delays in access are now contingent upon pCPA deciding whether to negotiate price and then the duration of any negotiation, and (iii) real-world evidence is no longer part of the decision-making for conditional approvals. A slight increase in the positive endorsement of RWE used to support CADTH recommendations was observed. Conclusions: The lack of timely access to oncology drugs hurts Canadian patients. While a small trend of improvement appears to be emerging, longer-term data collection is required to ensure sustained patient benefits. Full article
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<p>Approval status of oncology drugs approved from 2019 to June 2024. The analysis from 2023 to 30 June 2024 covers an eighteen months period.</p>
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27 pages, 615 KiB  
Article
A Multiparty Quantum Private Equality Comparison Scheme Relying on |GHZ3⟩ States
by Theodore Andronikos and Alla Sirokofskich
Future Internet 2024, 16(9), 309; https://doi.org/10.3390/fi16090309 - 27 Aug 2024
Viewed by 3687
Abstract
In this work, we present a new protocol that accomplishes multiparty quantum private comparison leveraging maximally entangled |GHZ3 triplets. Our intention was to develop a protocol that can be readily executed by contemporary quantum computers. This is possible [...] Read more.
In this work, we present a new protocol that accomplishes multiparty quantum private comparison leveraging maximally entangled |GHZ3 triplets. Our intention was to develop a protocol that can be readily executed by contemporary quantum computers. This is possible because the protocol uses only |GHZ3 triplets, irrespective of the number n of millionaires. Although it is feasible to prepare multiparticle entangled states of high complexity, this is overly demanding on a contemporary quantum apparatus, especially in situations involving multiple entities. By relying exclusively on |GHZ3 states, we avoid these drawbacks and take a decisive step toward the practical implementation of the protocol. An important quantitative characteristic of the protocol is that the required quantum resources are linear both in the number of millionaires and the amount of information to be compared. Additionally, our protocol is suitable for both parallel and sequential execution. Ideally, its execution is envisioned to take place in parallel. Nonetheless, it is also possible to be implemented sequentially if the quantum resources are insufficient. Notably, our protocol involves two third parties, as opposed to a single third party in the majority of similar protocols. Trent, commonly featured in previous multiparty protocols, is now accompanied by Sophia. This dual setup allows for the simultaneous processing of all n millionaires’ fortunes. The new protocol does not rely on a quantum signature scheme or pre-shared keys, reducing complexity and cost. Implementation wise, uniformity is ensured as all millionaires use similar private circuits composed of Hadamard and CNOT gates. Lastly, the protocol is information-theoretically secure, preventing outside parties from learning about fortunes or inside players from knowing each other’s secret numbers. Full article
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<p>This figure visualizes the fact that in every triplet of quantum registers <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>T</mi> <mi>I</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>S</mi> <mi>I</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>A</mi> <mi>I</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </semantics></math>, the <span class="html-italic">m</span> qubits in the corresponding positions belong to the same <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <mrow> <mi>G</mi> <mi>H</mi> <msub> <mi>Z</mi> <mn>3</mn> </msub> </mrow> <mrow> <mo>〉</mo> </mrow> </mrow> </semantics></math> triplet. To make this point clear, they are drawn with the same color.</p>
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<p>The above figure presents the block diagram of the GHZ<sub>3</sub>MQPEC protocol. For the acronyms appearing in the figure, we refer to <a href="#futureinternet-16-00309-t001" class="html-table">Table 1</a>.</p>
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<p>The above circuit <math display="inline"><semantics> <mrow> <mi>Q</mi> <msub> <mi>C</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>≤</mo> <mi>i</mi> <mo>≤</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>, embeds Alice<sub><span class="html-italic">i</span></sub>’s fortune <math display="inline"><semantics> <msub> <mi mathvariant="bold">f</mi> <mi>i</mi> </msub> </semantics></math> and Sophia’s secret number <math display="inline"><semantics> <mi mathvariant="bold">s</mi> </semantics></math> into the global state of the system. The potentially spatially separated private circuits operated by Alice<sub><span class="html-italic">i</span></sub>, Sophia, and Trent are linked due to entanglement, indicated by the wavy red line connecting <math display="inline"><semantics> <mrow> <mi>T</mi> <mi>I</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>S</mi> <mi>I</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>I</mi> <msub> <mi>R</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, and form one composite system.</p>
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<p>In the ideal scenario, the GHZ<sub>3</sub>MQPEC protocol can be executed entirely in parallel by employing a parallel array of <span class="html-italic">n</span> circuits <math display="inline"><semantics> <mrow> <mi>Q</mi> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>Q</mi> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>If the lack of resources precludes the parallel implementation of the protocol, the <span class="html-italic">n</span> circuits <math display="inline"><semantics> <mrow> <mi>Q</mi> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>Q</mi> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> can be partitioned in sequential batches. In this example, <math display="inline"><semantics> <mrow> <mi>Q</mi> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>Q</mi> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> are partitioned into 3 batches. The circuits within each batch are employed simultaneously, but the 3 batches are executed sequentially.</p>
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<p>This circuit, created with Qiskit, implements the GHZ<sub>3</sub>MQPEC protocol for 3 millionaires, Alice<sub>0</sub>, Alice<sub>1</sub>, and Alice<sub>2</sub>. Their fortunes were chosen so that they can be represented with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> qubits.</p>
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<p>This figure contains a few potential measurements and their associated probabilities for the circuit shown in <a href="#futureinternet-16-00309-f006" class="html-fig">Figure 6</a>.</p>
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<p>The above circuit embeds Alice and Bob’s fortunes <math display="inline"><semantics> <msub> <mi mathvariant="bold">f</mi> <mi>A</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold">f</mi> <mi>B</mi> </msub> </semantics></math> into the entangled system. The private circuits operated by Alice, Bob, and Trent are linked due to entanglement, indicated by the wavy red line connecting <math display="inline"><semantics> <mrow> <mi>T</mi> <mi>I</mi> <mi>R</mi> <mo>,</mo> <mi>A</mi> <mi>I</mi> <mi>R</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>I</mi> <mi>R</mi> </mrow> </semantics></math>, and form one composite system.</p>
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18 pages, 3533 KiB  
Article
Rice Yield Forecasting Using Hybrid Quantum Deep Learning Model
by De Rosal Ignatius Moses Setiadi, Ajib Susanto, Kristiawan Nugroho, Ahmad Rofiqul Muslikh, Arnold Adimabua Ojugo and Hong-Seng Gan
Computers 2024, 13(8), 191; https://doi.org/10.3390/computers13080191 - 7 Aug 2024
Cited by 1 | Viewed by 2228
Abstract
In recent advancements in agricultural technology, quantum mechanics and deep learning integration have shown promising potential to revolutionize rice yield forecasting methods. This research introduces a novel Hybrid Quantum Deep Learning model that leverages the intricate processing capabilities of quantum computing combined with [...] Read more.
In recent advancements in agricultural technology, quantum mechanics and deep learning integration have shown promising potential to revolutionize rice yield forecasting methods. This research introduces a novel Hybrid Quantum Deep Learning model that leverages the intricate processing capabilities of quantum computing combined with the robust pattern recognition prowess of deep learning algorithms such as Extreme Gradient Boosting (XGBoost) and Bidirectional Long Short-Term Memory (Bi-LSTM). Bi-LSTM networks are used for temporal feature extraction and quantum circuits for quantum feature processing. Quantum circuits leverage quantum superposition and entanglement to enhance data representation by capturing intricate feature interactions. These enriched quantum features are combined with the temporal features extracted by Bi-LSTM and fed into an XGBoost regressor. By synthesizing quantum feature processing and classical machine learning techniques, our model aims to improve prediction accuracy significantly. Based on measurements of mean square error (MSE), the coefficient of determination (R2), and mean average error (MAE), the results are 1.191621 × 10−5, 0.999929482, and 0.001392724, respectively. This value is so close to perfect that it helps make essential decisions in global agricultural planning and management. Full article
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<p>Plot the relationship of crop yield features with other features. (<b>a</b>) The relationship between crop yield and annual rainfall indicates no clear linear pattern, suggesting a complex or non-linear relationship influenced by other variables. (<b>b</b>) The relationship between crop yield and pesticide use also shows no strong linear pattern, indicating other factors may play a significant role. (<b>c</b>) The relationship between crop yield and average temperature does not show a clear linear relationship, suggesting temperature influences crop yield in a complex manner.</p>
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<p>Temporal feature analysis plot using a three-year moving average.</p>
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<p>Heatmap plot feature analysis.</p>
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<p>Framework of hybrid quantum–classical deep learning model.</p>
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<p>Quantum circuit design for feature processing.</p>
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<p>Sample dataset after one-hot encoding.</p>
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<p>Scatter plot of proposed regression model results.</p>
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21 pages, 387 KiB  
Article
Reading Refugee/(Im)Migrant Education Diffractively: Transdisciplinary Exploration of Matters That Matter and Matter That Matters in Refugee/(Im)Migrant Education
by Julie Kasper
Soc. Sci. 2024, 13(6), 284; https://doi.org/10.3390/socsci13060284 - 27 May 2024
Viewed by 928
Abstract
This paper is a conceptual exploration and diffractive reading of refugee/(im)migrant education through multiple lenses, including data-driven decision making, critical refugee studies, new materialism and critical feminist and posthumanist studies, and trans theorizations such as Black trans feminism. After a brief introduction to [...] Read more.
This paper is a conceptual exploration and diffractive reading of refugee/(im)migrant education through multiple lenses, including data-driven decision making, critical refugee studies, new materialism and critical feminist and posthumanist studies, and trans theorizations such as Black trans feminism. After a brief introduction to “the field” of refugee/(im)migrant education, the paper turns to diffractive readings of refugee/(im)migrant education as means of exploring what is the matter, as in the material and discursive substance, in refugee/(im)migrant education, and why and how (including when, where, and by whom) does that matter come to matter? The paper concludes with discoveries, or findings, from this diffractive, transdisciplinary exploration and considerations for educators, policymakers, researchers, activists, and other actors (co)constituting and “becoming with” refugee/(im)migrant education. Full article
20 pages, 1772 KiB  
Review
Sarcoidosis-Associated Pulmonary Hypertension
by Dominique Israël-Biet, Jean Pastré and Hilario Nunes
J. Clin. Med. 2024, 13(7), 2054; https://doi.org/10.3390/jcm13072054 - 2 Apr 2024
Viewed by 2653
Abstract
Sarcoidosis-associated pulmonary hypertension (SAPH) is a very severe complication of the disease, largely impacting its morbidity and being one of its strongest predictors of mortality. With the recent modifications of the hemodynamic definition of pulmonary hypertension (mean arterial pulmonary pressure >20 instead of [...] Read more.
Sarcoidosis-associated pulmonary hypertension (SAPH) is a very severe complication of the disease, largely impacting its morbidity and being one of its strongest predictors of mortality. With the recent modifications of the hemodynamic definition of pulmonary hypertension (mean arterial pulmonary pressure >20 instead of <25 mmHg,) its prevalence is presently not precisely known, but it affects from 3 to 20% of sarcoid patients; mostly, although not exclusively, those with an advanced, fibrotic pulmonary disease. Its gold-standard diagnostic tool remains right heart catheterization (RHC). The decision to perform it relies on an expert decision after a non-invasive work-up, in which echocardiography remains the screening tool of choice. The mechanisms underlying SAPH, very often entangled, are crucial to define, as appropriate and personalized therapeutic strategies will aim at targeting the most significant ones. There are no recommendations so far as to the indications and modalities of the medical treatment of SAPH, which is based upon the opinion of a multidisciplinary team of sarcoidosis, pulmonary hypertension and sometimes lung transplant experts. Full article
(This article belongs to the Special Issue Advances in the Diagnosis and Treatment of Pulmonary Sarcoidosis)
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<p>Clinical classification of pulmonary hypertension from [<a href="#B29-jcm-13-02054" class="html-bibr">29</a>].</p>
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<p>Multifactorial mechanisms lead to pulmonary hypertension in sarcoidosis and may include hypoxic vasoconstriction, pulmonary vascular rarefaction, parenchymal destruction, left heart disease with postcapillary PH, portal hypertension from liver disease, pulmonary vascular remodeling, changes resembling pulmonary veno-occlusive disease and extrinsic vascular compression due to fibrosing mediastinitis or enlarged lymph nodes.</p>
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<p>Proposed therapeutic approach of SAPH based on the mechanisms and phenotypes involved. * The therapeutic approach should be multidisciplinary, involving a sarcoidosis and a PH expert, and take into account the mechanisms involved in the development of PH, the severity of PH and the severity of the underlying parenchymal lung disease. <sup>†</sup> Anti-inflammatory treatment can be initiated before PAH-targeted therapy or in parallel. <sup>¶</sup> Referral for lung transplantation should not be delayed. Abbreviations: SAPH: sarcoidosis-associated pulmonary hypertension, CTA: computed tomography angiography, V/Q: ventilation/perfusion, AC: anticoagulant, CTEPH: chronic thromboembolic pulmonary hypertension, FVC: forced vital capacity, 18FDG-PET: 18F-2-fluoro-2-deoxy-D-glucose positron emission tomography, PVR: pulmonary vascular resistance, PAH: pulmonary arterial hypertension.</p>
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16 pages, 5250 KiB  
Article
Modeling Robotic Thinking and Creativity: A Classic–Quantum Dialogue
by Maria Mannone, Antonio Chella, Giovanni Pilato, Valeria Seidita, Filippo Vella and Salvatore Gaglio
Mathematics 2024, 12(5), 642; https://doi.org/10.3390/math12050642 - 22 Feb 2024
Cited by 1 | Viewed by 1697
Abstract
The human mind can be thought of as a black box, where the external inputs are elaborated in an unknown way and lead to external outputs. D’Ariano and Faggin schematized thinking and consciousness through quantum state dynamics. The complexity of mental states can [...] Read more.
The human mind can be thought of as a black box, where the external inputs are elaborated in an unknown way and lead to external outputs. D’Ariano and Faggin schematized thinking and consciousness through quantum state dynamics. The complexity of mental states can be formalized through the entanglement of the so-called qualia states. Thus, the interaction between the mind and the external world can be formalized as an interplay between classical and quantum-state dynamics. Since quantum computing is more and more often being applied to robots, and robots constitute a benchmark to test schematic models of behavior, we propose a case study with a robotic dance, where the thinking and moving mechanisms are modeled according to quantum–classic decision making. In our research, to model the elaboration of multi-sensory stimuli and the following decision making in terms of movement response, we adopt the D’Ariano–Faggin formalism and propose a case study with improvised dance based on a collection of poses, whose combination is presented in response to external and periodic multi-sensory stimuli. We model the dancer’s inner state and reaction to classic stimuli through a quantum circuit. We present our preliminary results, discussing further lines of development. Full article
(This article belongs to the Topic Quantum Information and Quantum Computing, 2nd Volume)
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<p>A schematic representation of classic–quantum information exchange.</p>
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<p>A pictorial representation of classic incoming multisensory stimuli, quantum thinking of the robot, and classical action as the response. The spectrograms refers to audio stimuli used in a color-timbre experiment [<a href="#B14-mathematics-12-00642" class="html-bibr">14</a>], and the “response” poses of the robot Pepper are taken from [<a href="#B15-mathematics-12-00642" class="html-bibr">15</a>]. The stimulus <span class="html-italic">red</span> is associated with a <span class="html-italic">forte</span> of orchestra with brass in evidence; the stimulus <span class="html-italic">grey</span> is associated with a softer orchestration with <span class="html-italic">pianissimo</span> winds and violins, and stimulus <span class="html-italic">black</span> is associated with a low-register <span class="html-italic">fortissimo</span> piano cluster.</p>
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<p>A pictorial representation of the complete cycle of our proposed model, a first external multisensory stimuli, a response from the robot after a step of quantum thinking, feedback from the external environment (which can be independent from the robotic action), and another sequence of quantum thinking and classic action from the robot, which becomes less and less predictable accordingly and more and more mixed. The pictures of the expressive poses of the robot Pepper are taken from [<a href="#B15-mathematics-12-00642" class="html-bibr">15</a>].</p>
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<p>Quantum circuit designed for our tests. Qubits <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> are initialized with the states of the auditory and visual stimuli, respectively, while qubit <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math> is initialized with the (initial) inner state of the dancer.</p>
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<p>Scheme of robotic actions associated with the outcome of quantum measurements, environmental (world) feedback in the form of new incoming multi-sensory stimuli for the robot, robotic elaboration of the stimuli as inner perception. The scheme can be reiterated, leading to less and less predictable behavior of the robot. For this reason, this toy model may approximate the creative behavior of an improvising dancer. Here, the notation is still derived by [<a href="#B6-mathematics-12-00642" class="html-bibr">6</a>]. At the inner-robotic level (quantum domain), the quantum operator <math display="inline"><semantics> <msub> <mi>M</mi> <mi>k</mi> </msub> </semantics></math> is followed by <math display="inline"><semantics> <msup> <mi>H</mi> <mrow> <mi>f</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> </semantics></math>, where the apex function <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </semantics></math> depends on the pedex of the first operator, transformed through the function <span class="html-italic">f</span>, which takes into account the feedback provided by the world. This is the very general scheme which can be instantiated as shown in <a href="#mathematics-12-00642-t003" class="html-table">Table 3</a>.</p>
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8 pages, 1781 KiB  
Article
Local Entanglement of Electrons in 1D Hydrogen Molecule
by Ivan P. Christov
Entropy 2023, 25(9), 1308; https://doi.org/10.3390/e25091308 - 8 Sep 2023
Viewed by 1498
Abstract
The quantum entanglement entropy of the electrons in a one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the [...] Read more.
The quantum entanglement entropy of the electrons in a one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the local entropy remains peaked in the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where a stable hydrogen molecule is formed, the quantum entropy shows no peculiarity thus indicating that the entropy and the energy measures display different sensitivity with respect to the interaction between the two identical electrons involved. One possible explanation is that the calculation of the quantum entropy does not account explicitly for the distance between the nuclei, which contrasts to the total energy calculation where the energy minimum depends decisively on that distance. The numerically exact and the time-dependent quantum Monte Carlo calculations show close results. Full article
(This article belongs to the Special Issue Editorial Board Members' Collection Series on Quantum Entanglement)
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<p>Walker distribution in configuration space for molecule of two 1D hydrogen atoms at a distance 3a.u. (<b>a</b>); contour maps of the reduced density matrix (<b>b</b>). Blue lines and points—exact result; red lines and points—from TDQMC.</p>
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<p>Ground state energy of hydrogen molecule (<b>a</b>) and global linear entropy (<b>b</b>) as function of the internuclear distance. Blue lines—exact result; red lines—from TDQMC. The green line in (<b>b</b>) shows the peak value of the local entropy, multiplied by 10.</p>
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<p>Partition of the 2D configuration space used in the calculations (<b>a</b>); (<b>b</b>) local linear entropy for different inter-nuclear distance d: d = 0—blue line; d = 3a.u.—green line; and d = 5a.u.—red line. Solid lines—exact results; dashed lines—TDQMC results.</p>
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29 pages, 1415 KiB  
Article
Adoption of Plant-Based Diets: A Process Perspective on Adopters’ Cognitive Propensity
by Fatima Canseco-Lopez and Francesc Miralles
Sustainability 2023, 15(9), 7577; https://doi.org/10.3390/su15097577 - 5 May 2023
Cited by 1 | Viewed by 3554
Abstract
Although there is great interest on the global stage in promoting plant-based diets (PBDs) to achieve some of the Sustainable Development Goals (SDGs), the results of their adoption are unsatisfactory. Academics propose to entangle this effort by addressing the challenges of dissemination of [...] Read more.
Although there is great interest on the global stage in promoting plant-based diets (PBDs) to achieve some of the Sustainable Development Goals (SDGs), the results of their adoption are unsatisfactory. Academics propose to entangle this effort by addressing the challenges of dissemination of social innovations (SIs). SIs generate different adoption attitudes, some of them related to socio-psychological aspects on the part of potential adopters. This research work aims to better understand the adoption of SIs, such as PBDs, which may induce socio-psychological concerns in potential adopters. In this sense, this research postulates that current perspectives on the dissemination and adoption of SI offer partial insights into understanding the shift to PBD. To overcome these limitations, a holistic process perspective of the adopter’s decision-making to change diet is derived and proposed. An exploratory, abductive, and theory-building effort has been carried out, based on a cross-analysis of three different adopter profiles, with a total of 69 semi-structured interviews. A new model for a comprehensive understanding from the adopter’s perspective on dietary change is outlined with new socio-psychological insights emerging from the adopter’s viewpoint. Additionally, the new model offers renewed opportunities for practitioners in terms of PBD implementation, usage, and policy. Full article
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<p>Contextual description of the proposed conceptual framework.</p>
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<p>A high-level perspective of the conceptual framework on the PBD adoption.</p>
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<p>Mediation effects of facilitators and barriers in each stage of the adoption process.</p>
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<p>Moderating and mediating elements that influence the potential adopter’s propensity to cognitive consistency.</p>
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<p>A process perspective of PBD adoption.</p>
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22 pages, 825 KiB  
Article
Quantum Circuit Components for Cognitive Decision-Making
by Dominic Widdows, Jyoti Rani and Emmanuel M. Pothos
Entropy 2023, 25(4), 548; https://doi.org/10.3390/e25040548 - 23 Mar 2023
Cited by 8 | Viewed by 8733
Abstract
This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order [...] Read more.
This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer ‘yes’ or ‘no’, so the population that answers ‘yes’ to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations. Full article
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<p>Non-commutative projections model the order effect in the Clinton–Gore scenario. We see that the projection of the |0〉 vector onto the <span class="html-italic">Clinton</span> axis gives a point further from the origin if we first project onto the <span class="html-italic">Gore</span> axis (<b>right</b>) rather than if we just project the |0〉 vector onto the <span class="html-italic">Clinton</span> axis (<b>left</b>). These diagrams show only the quadrant with positive real coordinates, so if the <span class="html-italic">Gore</span> axis is at angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> above the horizontal, it appears at the point <math display="inline"><semantics> <mrow> <mo form="prefix">cos</mo> <mo>(</mo> <mi>θ</mi> <mo>)</mo> <mo>|</mo> <mn>0</mn> <mi>〉</mi> <mo>+</mo> <mo form="prefix">sin</mo> <mo>(</mo> <mi>θ</mi> <mo>)</mo> <mo>|</mo> <mn>1</mn> <mi>〉</mi> </mrow> </semantics></math>. In reality, the coordinates can be any complex numbers <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>β</mi> </semantics></math> such that <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msup> <mi>α</mi> <mn>2</mn> </msup> <mrow> <mo>|</mo> <mo>+</mo> <mo>|</mo> </mrow> <msup> <mi>β</mi> <mn>2</mn> </msup> <mrow> <mo>|</mo> <mo>=</mo> <mn>1</mn> </mrow> </mrow> </semantics></math>.</p>
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<p>Bloch sphere representation of a qubit. (From <a href="https://en.wikipedia.org/wiki/Bloch_sphere" target="_blank">https://en.wikipedia.org/wiki/Bloch_sphere</a>, Creative Commons CC BY-SA 3.0 license. Accessed on 14 March 2023).</p>
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<p>Basic quantum logic gate diagrams used throughout these examples. A single-qubit rotation gate manipulates the superposition of |0〉 and |1〉 states for the qubit. The two-qubit CNOT gate (right) entangles two qubits (the top qubit is the control qubit and the bottom is the target qubit). The swap gate swaps the states of the two qubits. The measurement operator measures the qubit’s value and stores it in the given classical bit.</p>
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<p>Circuit for setting probability of single event <span class="html-italic">A</span>.</p>
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<p>Bloch sphere vectors for Clinton and Gore.</p>
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<p>Circuits implementing the Clinton–Gore order effects, with and without mid-measurement.</p>
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<p>Order effect circuit with an extra qubit <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math> that controls whether or not the participant is asked the first question.</p>
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<p>Circuit for setting conditional probability. Note that the white circle means ‘if this qubit is in state |0〉’ and the black circle means ’if this qubit is in state |1〉’.</p>
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<p>Circuit implementing a simple classical Bayesian network.</p>
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<p>Schematic diagram of a Mach–Zehnder Interferometer.</p>
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<p>Circuit for simulating interference between unknown outcomes. The ‘H’ gate is a Hadamard gate which maps the state |0〉 to a superposition state <math display="inline"><semantics> <mrow> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mrow> <mo>(</mo> <mo>|</mo> <mn>0</mn> <mi>〉</mi> <mo>+</mo> <mo>|</mo> <mn>1</mn> <mi>〉</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and |1〉 to the state <math display="inline"><semantics> <mrow> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mrow> <mo>(</mo> <mo>|</mo> <mn>0</mn> <mi>〉</mi> <mo>−</mo> <mo>|</mo> <mn>1</mn> <mi>〉</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Different output probabilities for the target qubit as a function of the phase angle <math display="inline"><semantics> <mi>φ</mi> </semantics></math>, when the gates before and after the <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> operation of <a href="#entropy-25-00548-f011" class="html-fig">Figure 11</a> are changed.</p>
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<p>Circuit for conditional probability with interference.</p>
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<p>Outcome probabilities for the Prisoner’s Dilemma scenario.</p>
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<p>Swapping in ancillas as a proxy for mid-circuit measurement.</p>
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<p>Complete circuit simulating the Prisoner’s Dilemma scenario.</p>
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18 pages, 618 KiB  
Article
Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree
by Dongfen Li, Yundan Zheng, Xiaofang Liu, Jie Zhou, Yuqiao Tan, Xiaolong Yang and Mingzhe Liu
Mathematics 2022, 10(23), 4571; https://doi.org/10.3390/math10234571 - 2 Dec 2022
Cited by 2 | Viewed by 1489
Abstract
Quantum informatics is a new subject formed by the intersection of quantum mechanics and informatics. Quantum communication is a new way to transmit quantum states through quantum entanglement, quantum teleportation, and quantum information splitting. Based on the research of multiparticle state quantum information [...] Read more.
Quantum informatics is a new subject formed by the intersection of quantum mechanics and informatics. Quantum communication is a new way to transmit quantum states through quantum entanglement, quantum teleportation, and quantum information splitting. Based on the research of multiparticle state quantum information splitting, this paper innovatively combines the decision tree algorithm of machine learning with quantum communication to solve the problem of channel particle allocation in quantum communication, and experiments showed that the algorithm can make the optimal allocation scheme. Based on this scheme, we propose a two-particle state hierarchical quantum information splitting scheme based on the multi-particle state. First, Alice measures the Bell states of the particles she owns and tells the result to the receiver through the classical channel. If the receiver is a high-level communicator, he only needs the help of one of the low-level communicators and all the high-level communicators. After performing a single particle measurement on the z-basis, they send the result to the receiver through the classical channel. When the receiver is a low-level communicator, all communicators need to measure the particles they own and tell the receiver the results. Finally, the receiver performs the corresponding unitary operation according to the received results. In this regard, a complete hierarchical quantum information splitting operation is completed. On the basis of theoretical research, we also carried out experimental verification, security analysis, and comparative analysis, which shows that our scheme is reliable and has high security and efficiency. Full article
(This article belongs to the Special Issue Artificial Intelligence and Data Science)
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<p>Overall framework.</p>
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<p>Model 1.</p>
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<p>Model 1(a) limiting the number of leaf node samples.</p>
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<p>Model 2.</p>
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<p>Test set sample accuracy.</p>
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<p>Decision tree model 2(b) with minimum cross-validation error.</p>
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<p>Model 3. From left to right are (<b>a</b>) the generated decision model, (<b>b</b>) the decision model with the least value for the leaf node, (<b>c</b>) the decision model after pruning.</p>
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<p>The complete process of the experiment.</p>
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15 pages, 1233 KiB  
Concept Paper
Unleashing the Potentials of Quantum Probability Theory for Customer Experience Analytics
by Havana Rika, Itzhak Aviv and Roye Weitzfeld
Big Data Cogn. Comput. 2022, 6(4), 135; https://doi.org/10.3390/bdcc6040135 - 10 Nov 2022
Cited by 10 | Viewed by 2839
Abstract
In information systems research, the advantages of Customer Experience (CX) and its contribution to organizations are largely recognized. The CX analytics evaluate how customers perceive products, ranging from their functional usage to their cognitive states regarding the product, such as emotions, sentiment, and [...] Read more.
In information systems research, the advantages of Customer Experience (CX) and its contribution to organizations are largely recognized. The CX analytics evaluate how customers perceive products, ranging from their functional usage to their cognitive states regarding the product, such as emotions, sentiment, and satisfaction. The most recent research in psychology reveals that cognition analytics research based on Classical Probability Theory (CPT) and statistical learning, which is used to evaluate people’s cognitive states, is limited due to their reliance on rational decision-making. However, the cognitive attitudes of customers are characterized by uncertainty and entanglement, resulting in irrational decision-making bias. What is captured by traditional CPT-based data science in the context of cognition aspects of CX analytics is only a small portion of what should be captured. Current CX analytics efforts fall far short of their full potential. In this paper, we set a novel research direction for CX analytics by Quantum Probability Theory (QPT). QPT-based analytics have been introduced recently in psychology research and reveal better cognition assessment under uncertainty, with a high level of irrational behavior. Adopting recent advances in the psychology domain, this paper develops a vision and sets a research agenda for expanding the application of CX analytics by QPT to overcome CPT shortcomings, identifies research areas that contribute to the vision, and proposes elements of a future research agenda. To stimulate debate and research QPT-CX analytics, we attempt a preliminary characterization of the novel method by introducing a QPT-based rich mathematical framework for CX cognitive modeling based on quantum superposition, Bloch sphere, and Hilbert space. We demonstrate the implementation of the QPT-CX model by the use case of customers’ emotional motivator assessments while implementing quantum vector space with a set of mathematical axioms for CX analytics. Finally, we outline the key advantages of quantum CX over classical by supporting theoretical proof for each key. Full article
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<p>There are three questions, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, each with its own basis state <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>,</mo> <mo> </mo> <mi mathvariant="italic">and</mi> <mo> </mo> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> </semantics></math> together with their corresponding orthogonal vectors <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> <mo>,</mo> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> <mo>,</mo> <mo> </mo> <mi mathvariant="italic">and</mi> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math>, where each pair <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mi>i</mi> </msub> <mo> </mo> <mi mathvariant="italic">and</mi> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mi>i</mi> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math> spans a two-dimensional plane. <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo> </mo> <mi mathvariant="italic">and</mi> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math> are colored blue, <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo> </mo> <mi mathvariant="italic">and</mi> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math> are colored red, and <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>3</mn> </msub> <mo> </mo> <mi mathvariant="italic">and</mi> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </semantics></math> are colored black. The gray vectors, together with their orthogonal vectors, can potentially represent some additional other questions rather than the ones we presented before. The green vector represents the customer data during their digital purchases, and the dashed lines represent the projection on each of the three questions, which indicates the probability of each of these questions’ outcomes.</p>
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<p>Data sources for customer’s emotional motivator analytics.</p>
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<p>(<b>a</b>) Bloch sphere illustrated visually with two basis states |0⟩ and |1⟩ and a state vector |ψ⟩. (<b>b</b>) Bloch sphere with ten vectors representing all ten emotional motivator classes. Note that all their ten orthogonal vectors are omitted for simplicity.</p>
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<p>Denote by <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>ψ</mo> <mo>⟩</mo> </mrow> </semantics></math> the state vector, and let <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo>,</mo> <mtext> </mtext> <msub> <mi>Q</mi> <mn>2</mn> </msub> </mrow> </semantics></math> be two questions with their corresponding basis vectors <math display="inline"><semantics> <mrow> <mfenced close="}" open="{"> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>,</mo> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> <mo>,</mo> <mo> </mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>,</mo> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> <mo stretchy="false">¯</mo> </mover> </mrow> </mfenced> </mrow> </semantics></math>, and denote by <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Π</mi> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="sans-serif">Π</mi> </mrow> </mrow> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </semantics></math> their projectors. (<b>a</b>) The outcome when first asking <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and then <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> </mrow> </semantics></math> on the state vector, i.e., <math display="inline"><semantics> <mrow> <mo>‖</mo> <msub> <mi mathvariant="sans-serif">Π</mi> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>⋅</mo> <msub> <mi mathvariant="sans-serif">Π</mi> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>|</mo> <mo>ψ</mo> <mo>⟩</mo> <msup> <mo>‖</mo> <mn>2</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) The outcome when first asking <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> </mrow> </semantics></math> and then <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> </mrow> </semantics></math> on the state vector, i.e.,<math display="inline"><semantics> <mrow> <mo>‖</mo> <msub> <mi mathvariant="sans-serif">Π</mi> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>⋅</mo> <msub> <mi mathvariant="sans-serif">Π</mi> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>|</mo> <mo>ψ</mo> <mo>⟩</mo> <msup> <mo>‖</mo> <mn>2</mn> </msup> </mrow> </semantics></math>. In that case, <math display="inline"><semantics> <mrow> <mi>P</mi> <mfenced> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mtext> </mtext> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>n</mi> <mtext> </mtext> <msub> <mi>Q</mi> <mn>2</mn> </msub> </mrow> </mfenced> <mo>&lt;</mo> <mi>P</mi> <mfenced> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> <mtext> </mtext> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>n</mi> <mtext> </mtext> <msub> <mi>Q</mi> <mn>1</mn> </msub> </mrow> </mfenced> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) The probabilities of the events <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>,</mo> <mo> </mo> <mi>B</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>&amp;</mo> <mi>B</mi> </mrow> </semantics></math> in classical probability: <math display="inline"><semantics> <mrow> <mi>P</mi> <mfenced> <mi>A</mi> </mfenced> <mo>=</mo> <mn>0.6</mn> <mo>;</mo> <mo> </mo> <mi>P</mi> <mfenced> <mi>B</mi> </mfenced> <mo>=</mo> <mn>0.68</mn> <mo>;</mo> <mo> </mo> <mi>P</mi> <mfenced> <mrow> <mi>A</mi> <mo>&amp;</mo> <mi>B</mi> </mrow> </mfenced> <mo>=</mo> <mi>P</mi> <mfenced> <mrow> <mi>B</mi> <mo>&amp;</mo> <mi>A</mi> </mrow> </mfenced> <mo>=</mo> <mn>0.18</mn> </mrow> </semantics></math>, whereas (<b>b</b>) presents the same three events, but in terms of quantum probability, the length of the projection of the state vector (colored in green) onto each of the basis vectors <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>,</mo> <mo> </mo> <mi>B</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>&amp;</mo> <mi>B</mi> </mrow> </semantics></math> indicates the probability of each of them occurring according to the state vector.</p>
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10 pages, 1838 KiB  
Article
Model-Free Deep Recurrent Q-Network Reinforcement Learning for Quantum Circuit Architectures Design
by Tomah Sogabe, Tomoaki Kimura, Chih-Chieh Chen, Kodai Shiba, Nobuhiro Kasahara, Masaru Sogabe and Katsuyoshi Sakamoto
Quantum Rep. 2022, 4(4), 380-389; https://doi.org/10.3390/quantum4040027 - 21 Sep 2022
Cited by 4 | Viewed by 3648
Abstract
Artificial intelligence (AI) technology leads to new insights into the manipulation of quantum systems in the Noisy Intermediate-Scale Quantum (NISQ) era. Classical agent-based artificial intelligence algorithms provide a framework for the design or control of quantum systems. Traditional reinforcement learning methods are designed [...] Read more.
Artificial intelligence (AI) technology leads to new insights into the manipulation of quantum systems in the Noisy Intermediate-Scale Quantum (NISQ) era. Classical agent-based artificial intelligence algorithms provide a framework for the design or control of quantum systems. Traditional reinforcement learning methods are designed for the Markov Decision Process (MDP) and, hence, have difficulty in dealing with partially observable or quantum observable decision processes. Due to the difficulty of building or inferring a model of a specified quantum system, a model-free-based control approach is more practical and feasible than its counterpart of a model-based approach. In this work, we apply a model-free deep recurrent Q-network (DRQN) reinforcement learning method for qubit-based quantum circuit architecture design problems. This paper is the first attempt to solve the quantum circuit design problem from the recurrent reinforcement learning algorithm, while using discrete policy. Simulation results suggest that our long short-term memory (LSTM)-based DRQN method is able to learn quantum circuits for entangled Bell–Greenberger–Horne–Zeilinger (Bell–GHZ) states. However, since we also observe unstable learning curves in experiments, suggesting that the DRQN could be a promising method for AI-based quantum circuit design application, more investigation on the stability issue would be required. Full article
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Figure 1

Figure 1
<p>The setting of the proposed learning algorithm. (<bold>a</bold>) A LSTM cell and a feed-forward neural network (FNN) are used for history Q-function approximation. (<bold>b</bold>) The RL environment–agent diagram.</p>
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<p>Learning curves for 2-qubit Bell state generation. Each data point is the moving average of 2000 episodes, and the average value (solid line) with one standard deviation error bar (cyan color) over 10 independent curves are reported. (<bold>a</bold>) Reward is plotted against number of episodes; (<bold>b</bold>) number of steps to reach the goal is plotted against number of episodes.</p>
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<p>Learning curves for 3-qubit GHZ state generation. Each data point is the moving average of 2000 episodes, and the average value (solid line) with one standard deviation error bar (cyan color) over 10 independent curves is reported. (<bold>a</bold>) Reward is plotted against number of episodes; (<bold>b</bold>) number of steps to reach the goal is plotted against number of episodes.</p>
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<p>City diagrams for density matrices produced by the learning agent. The best result (highest fidelity) over 10 random seeds and 100 test steps of the policy obtained in the last episode is reported. (<bold>a</bold>) The 2-qubit Bell state experiment. The fidelity is 0.9698. (<bold>b</bold>) The 3-qubit GHZ state experiment. The fidelity is 0.6710.</p>
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<p>Histograms of maximum fidelity over 100 test steps for 10 independent samples. (<bold>a</bold>) The 2-qubit Bell state experiment. (<bold>b</bold>) The 3-qubit GHZ state experiment.</p>
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24 pages, 731 KiB  
Article
Estimation of the Influence of a Noisy Environment on the Binary Decision Strategy in a Quantum Illumination Radar
by Sylvain Borderieux, Arnaud Coatanhay and Ali Khenchaf
Sensors 2022, 22(13), 4821; https://doi.org/10.3390/s22134821 - 25 Jun 2022
Cited by 1 | Viewed by 1625
Abstract
A quantum illumination radar uses quantum entanglement to enhance photodetection sensitivity. The entanglement is quickly destroyed by the decoherence in an environment, although the sensitivity enhancement could survive thanks to quantum correlations beyond the entanglement. These quantum correlations are quantified by the quantum [...] Read more.
A quantum illumination radar uses quantum entanglement to enhance photodetection sensitivity. The entanglement is quickly destroyed by the decoherence in an environment, although the sensitivity enhancement could survive thanks to quantum correlations beyond the entanglement. These quantum correlations are quantified by the quantum discord. Here, we use a toy model with an amplitude damping channel and Lloyd’s binary decision strategy to highlight the possible role of these correlations from the perspective of a quantum radar. Full article
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Figure 1

Figure 1
<p>The quantum illumination radar process has three steps. In Step 1, the entangled pair of photons is created inside the radar. In Step 2, we perform a separation. In 2a, the blue photon is trapped inside the radar, while in step 2b, the red photon propagates through a medium before being reflected by the target. The red photon returns to the receiver. In step 3, the pair of photons is gathered, and a joint measurement of the quantum state blue–red is taken.</p>
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<p>The entanglement rate and of the quantum discord as functions of the parameter <math display="inline"><semantics> <mrow> <mi mathvariant="normal">z</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math> for a Werner state <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mi mathvariant="normal">w</mi> </msub> <mo>=</mo> <mi mathvariant="normal">z</mi> <mfenced separators="" open="|" close="&#x232A;"> <msup> <mi mathvariant="normal">Ψ</mi> <mo>−</mo> </msup> </mfenced> <msub> <mfenced separators="" open="&#x2329;" close="|"> <msup> <mi mathvariant="normal">Ψ</mi> <mo>−</mo> </msup> </mfenced> <mi>AS</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>−</mo> <mi mathvariant="normal">z</mi> <mo>)</mo> </mrow> <mo>/</mo> <mn>4</mn> <msub> <mover accent="true"> <mi>I</mi> <mo>^</mo> </mover> <mi>AS</mi> </msub> </mrow> </semantics></math>. The entanglement rate <math display="inline"><semantics> <mrow> <mi mathvariant="script">E</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mi mathvariant="normal">w</mi> </msub> <mo>)</mo> </mrow> </semantics></math> is in brown, and the concurrence <math display="inline"><semantics> <mrow> <mi mathvariant="script">C</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mi mathvariant="normal">w</mi> </msub> <mo>)</mo> </mrow> </semantics></math> is red. The quantum discord <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mi mathvariant="normal">w</mi> </msub> <mo>)</mo> </mrow> </semantics></math> in blue represents the number of quantum correlations.</p>
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<p>The concurrence of Wootters <math display="inline"><semantics> <mrow> <mi mathvariant="script">C</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> in green and the entanglement rate <math display="inline"><semantics> <mrow> <mi mathvariant="script">E</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> in red as functions of the parameter <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>The Von Neumann entropy <math display="inline"><semantics> <mrow> <mi mathvariant="script">S</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> </mrow> </msub> <mspace width="4.pt"/> <mi>out</mi> <mo>)</mo> </mrow> </semantics></math> of the system AS in red and the conditional entropy <math display="inline"><semantics> <mrow> <mi mathvariant="script">S</mi> <msub> <mrow> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>|</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi mathvariant="normal">S</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>{</mo> <msubsup> <mover accent="true"> <mi>M</mi> <mo>^</mo> </mover> <mi mathvariant="normal">S</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>}</mo> </mrow> </msub> </mrow> </semantics></math> in green as functions of parameter <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>The quantum mutual information <math display="inline"><semantics> <mrow> <mi mathvariant="script">I</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> in blue and the classical information <math display="inline"><semantics> <mrow> <mi mathvariant="script">J</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> in red as functions of the parameter <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>The entanglement rate <math display="inline"><semantics> <mrow> <mi mathvariant="script">E</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> (red), the concurrence of Wooters <math display="inline"><semantics> <mrow> <mi mathvariant="script">C</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> (green), and the quantum discord <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>(</mo> <msub> <mover accent="true"> <mi>ρ</mi> <mo>^</mo> </mover> <mrow> <mi>AS</mi> <mo>,</mo> <mi>out</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> (blue) as functions of the parameter <span class="html-italic">p</span> for <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>Detection strategies for the hypotheses <math display="inline"><semantics> <msub> <mi>H</mi> <mn>0</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>H</mi> <mn>1</mn> </msub> </semantics></math> in Lloyd’s binary decision strategy for both single-photon and QI radars. When an object can be detected, we are in hypothesis <math display="inline"><semantics> <msub> <mi>H</mi> <mn>1</mn> </msub> </semantics></math>. In hypothesis <math display="inline"><semantics> <msub> <mi>H</mi> <mn>0</mn> </msub> </semantics></math>, only thermal photons can be detected, since no object is present.</p>
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<p>The <math display="inline"><semantics> <msub> <mi>SNR</mi> <mo>+</mo> </msub> </semantics></math> in the QI radar as a function of the parameter <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </semantics></math> with <math display="inline"><semantics> <msub> <mi>n</mi> <mi>b</mi> </msub> </semantics></math> calculated for <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>5</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>14</mn> </msup> </mrow> </semantics></math> Hz. The SNR has been normalized by its maximum because as the noise <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>b</mi> </msub> <mo>≪</mo> <mn>1</mn> </mrow> </semantics></math>, the SNR is huge for small values of <span class="html-italic">p</span>.</p>
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