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10 pages, 2009 KiB  
Brief Report
Challenges and Solutions for Secure Key Management and Monitoring: Review of the Cerberis3 Quantum Key Distribution System
by Ints Meijers
Quantum Rep. 2024, 6(3), 426-435; https://doi.org/10.3390/quantum6030027 - 13 Aug 2024
Viewed by 930
Abstract
Quantum Key Distribution (QKD) offers a revolutionary approach to secure communication, leveraging the principles of quantum mechanics to generate and distribute cryptographic keys that are immune to eavesdropping. As QKD systems become more widely adopted, the need for robust monitoring and management solutions [...] Read more.
Quantum Key Distribution (QKD) offers a revolutionary approach to secure communication, leveraging the principles of quantum mechanics to generate and distribute cryptographic keys that are immune to eavesdropping. As QKD systems become more widely adopted, the need for robust monitoring and management solutions has become increasingly crucial. The Cerberis3 QKD system from ID Quantique addresses this challenge by providing a comprehensive monitoring and visualization platform. The system’s advanced features, including central configuration, SNMP integration, and the graphical visualization of key performance metrics, enable network administrators to ensure their QKD infrastructure’s reliable and secure operation. Monitoring critical parameters such as Quantum Bit Error Rate (QBER), secret key rate, and link visibility is essential for maintaining the integrity of the quantum channel and optimizing the system’s performance. The Cerberis3 system’s ability to interface with encryption vendors and support complex network topologies further enhances its versatility and integration capabilities. By addressing the unique challenges of quantum monitoring, the Cerberis3 system empowers organizations to leverage the power of QKD technology, ensuring the security of their data in the face of emerging quantum computing threats. This article explores the Cerberus3 system’s features and its role in overcoming the monitoring challenges inherent to QKD deployments. Full article
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Figure 1

Figure 1
<p>Experimental setup diagram.</p>
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<p>Key rate.</p>
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<p>QBER.</p>
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<p>Visibility.</p>
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<p>Detections.</p>
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<p>Compression.</p>
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22 pages, 914 KiB  
Article
Estimating Interception Density in the BB84 Protocol: A Study with a Noisy Quantum Simulator
by Francesco Fiorini, Michele Pagano, Rosario Giuseppe Garroppo and Antonio Osele
Future Internet 2024, 16(8), 275; https://doi.org/10.3390/fi16080275 - 2 Aug 2024
Viewed by 4999
Abstract
Quantum computers have the potential to break the public-key cryptosystems widely used in key exchange and digital signature applications. To address this issue, quantum key distribution (QKD) offers a robust countermeasure against quantum computer attacks. Among various QKD schemes, BB84 is the most [...] Read more.
Quantum computers have the potential to break the public-key cryptosystems widely used in key exchange and digital signature applications. To address this issue, quantum key distribution (QKD) offers a robust countermeasure against quantum computer attacks. Among various QKD schemes, BB84 is the most widely used and studied. However, BB84 implementations are inherently imperfect, resulting in quantum bit error rates (QBERs) even in the absence of eavesdroppers. Distinguishing between QBERs caused by eavesdropping and QBERs due to channel imperfections is fundamentally infeasible. In this context, this paper proposes and examines a practical method for detecting eavesdropping via partial intercept-and-resend attacks in the BB84 protocol. A key feature of the proposed method is its consideration of quantum system noise. The efficacy of this method is assessed by employing the Quantum Solver library in conjunction with backend simulators inspired by real quantum machines that model quantum system noise. The simulation outcomes demonstrate the method’s capacity to accurately estimate the eavesdropper’s interception density in the presence of system noise. Moreover, the results indicate that the estimation accuracy of the eavesdropper’s interception density in the presence of system noise is dependent on both the actual interception density value and the key length. Full article
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Figure 1

Figure 1
<p>BB84 flowchart.</p>
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<p>BB84 key generation.</p>
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<p>BB84 key checking.</p>
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<p>BB84 validation.</p>
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<p>Case 1: without Eve.</p>
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<p>Case 2: with Eve.</p>
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<p>Scenario with interception density <span class="html-italic">p</span>.</p>
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<p><tt>aer_simulator</tt> model, <span class="html-italic">n</span> = 1024.</p>
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<p><tt>aer_simulator</tt> model, <span class="html-italic">n</span> = 4096.</p>
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<p><tt>fake_brooklin</tt> simulator model, <span class="html-italic">n</span> = 1024.</p>
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<p><tt>fake_brooklin</tt> simulator model, <span class="html-italic">n</span> = 4096.</p>
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<p>Estimated <span class="html-italic">p</span> with <tt>fake_brooklin</tt> simulator, <span class="html-italic">n</span> = 1024.</p>
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<p>Estimated <span class="html-italic">p</span> with <tt>fake_brooklin</tt> simulator, <span class="html-italic">n</span> = 4096.</p>
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29 pages, 5992 KiB  
Article
Toward Converged Satellite/Fiber 1550 nm DS-BB84 QKD Networks: Feasibility Analysis and System Requirements
by Aristeidis Stathis, Argiris Ntanos, Nikolaos K. Lyras, Giannis Giannoulis, Athanasios D. Panagopoulos and Hercules Avramopoulos
Photonics 2024, 11(7), 609; https://doi.org/10.3390/photonics11070609 - 27 Jun 2024
Cited by 1 | Viewed by 1452
Abstract
Satellite-based QKD is currently being developed to revolutionize global cryptographic key exchange by facilitating secure communication among remote parties at a global scale. By overcoming the exponential loss of fiber transmission, satellite-to-Earth communication can seamlessly interconnect vast distances as the link budget of [...] Read more.
Satellite-based QKD is currently being developed to revolutionize global cryptographic key exchange by facilitating secure communication among remote parties at a global scale. By overcoming the exponential loss of fiber transmission, satellite-to-Earth communication can seamlessly interconnect vast distances as the link budget of such links is sufficient to support QKD links. In terms of this direction, DV-QKD implementations seems to be technologically ahead since key exchange has been experimentally demonstrated to perform much more efficiently by providing key rates that are orders of magnitude higher compared to entanglement-based key exchange. However, the specific requirements to support effectively functional DV-QKD satellite-to-ground links are yet to be defined. This work attempts to define the satellite and ground segment system requirements needed in order to achieve functional QKD service for various satellites orbits (LEO, MEO, and GEO). Finite key size effects are being considered to determine the minimum block sizes that are required for secure key generation between a satellite node and a ground terminal for a single satellite pass. The atmospheric link channel is modeled with consideration of the most important degradation effects such as turbulence and atmospheric and pointing loss. Critical Tx and Rx system parameters, such as the source’s intrinsic Quantum Bit Error Rate (iQBER), the Rx telescope aperture size, and detection efficiency, were investigated in order to define the minimum requirements to establish an operation satellite-to-ground QKD link under specific assumptions. The performance of each downlink scenario was evaluated for the wavelength of 1550 nm in terms of link availability, link budget, and in the distilling of secure key volumes over time. Finally, the feasibility and requirements for distributing the collected space photons via terrestrial telecom fibers was also studied and discussed, leading to the proposal of a more futuristic WDM-enabled satellite QKD architecture. This comprehensive analysis aims to contribute to the advancement and implementation of effective satellite-based QKD systems, which can further exploit the ground fiber segment to realize converged space/terrestrial QKD networks. Full article
(This article belongs to the Section Quantum Photonics and Technologies)
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Figure 1
<p>Schematic of the envisioned architecture integrating urban and terrestrial grid networks across LEO, MEO, and GEO orbits for DS-BB84 QKD downlinks under night-time conditions. The fiber distribution routes from OGS to detection stations are illustrated with yellow lines.</p>
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<p>Flow chart of the satellite-to-ground MATLAB 2020 software calculator.</p>
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<p>End-to-end link loss over time, as well as the expected normalized SKR over time for different transmitted block sizes values, in telescope-to-SMF coupling, all while considering both (<b>a</b>) SNSPD detectors and (<b>b</b>) SPAD detectors.</p>
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<p>End-to-end link loss and normalized SKR over time for different transmitted block size values of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1 m and SNSPD with SMF coupling, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1.5 m and SNSPD with SMF coupling and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 2.3 m and SPAD without SMF coupling.</p>
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<p>End-to-end link loss and normalized SKR over time for different transmitted block size values of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1.5 m and SNSPD with SMF coupling, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 2.3 m and SNSPD with SMF coupling, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 2.3 m and SNSPDs without SMF coupling.</p>
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<p>End-to-end link loss and normalized SKR over time for the different i-QBER values of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1 m and SNSPD with SMF coupling, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1 m and SPAD with SMF coupling, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1 m and SPAD without SMF coupling.</p>
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<p>End-to-end link loss and normalized SKR over time for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> = 1 m and SNSPD with SMF coupling.</p>
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<p>SKR over time for a single satellite pass when varying the sky radiance values of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and SMF-coupled SNSPD detection, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and SMF-coupled SPAD detection, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and free-space SPAD detection.</p>
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<p>SKRs over a single MEO satellite pass when varying the sky radiance values of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and SMF-coupled SNSPD detection and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>2.3</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and SMF-coupled SNSPD detection.</p>
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<p>Contour plots of the SMF coupling loss (dB) over focal length Fr and receiver aperture diameter Dr for (<b>a</b>) full-AO correction, (<b>b</b>) tip–tilt correction for Cn<sup>2</sup> = 10<sup>−14</sup> m<sup>−2/3</sup>, and (<b>c</b>) tip–tilt correction for Cn<sup>2</sup> = 10<sup>−13</sup> m<sup>−2/3</sup> with an elevation angle of 90°.</p>
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<p>SKR over time for the different <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> values of (<b>a</b>) SNSPD with SMF coupling, (<b>b</b>) SPAD with SMF coupling, and (<b>c</b>) SPAD without SMF coupling.</p>
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<p>SKR over time accounting for the additional fiber distribution losses of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> with SNSPD detection, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>2.3</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> telescope receiver with SNSPD detection, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> telescope receiver with SPAD detection.</p>
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<p>SKR over time accounting for the additional fiber distribution losses of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>2.3</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> with SNSPD detection and full-AO correction for (<b>a</b>) LEO, (<b>b</b>) MEO, and (<b>c</b>) GEO cases.</p>
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<p>Yearly distilled key bit volume bar plot for LEO, MEO, and GEO.</p>
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<p>Multiple WDM-assisted, on-board QKD source architecture. The centralized SNSPD stations allowed for a significant boost in SKR.</p>
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22 pages, 2381 KiB  
Article
Quantum Authentication Evolution: Novel Approaches for Securing Quantum Key Distribution
by Hassan Termos
Entropy 2024, 26(6), 447; https://doi.org/10.3390/e26060447 - 26 May 2024
Cited by 1 | Viewed by 1530
Abstract
This study introduces a novel approach to bolstering quantum key distribution (QKD) security by implementing swift classical channel authentication within the SARG04 and BB84 protocols. We propose mono-authentication, a pioneering paradigm employing quantum-resistant signature algorithms—specifically, CRYSTALS-DILITHIUM and RAINBOW—to authenticate solely at the conclusion [...] Read more.
This study introduces a novel approach to bolstering quantum key distribution (QKD) security by implementing swift classical channel authentication within the SARG04 and BB84 protocols. We propose mono-authentication, a pioneering paradigm employing quantum-resistant signature algorithms—specifically, CRYSTALS-DILITHIUM and RAINBOW—to authenticate solely at the conclusion of communication. Our numerical analysis comprehensively examines the performance of these algorithms across various block sizes (128, 192, and 256 bits) in both block-based and continuous photon transmission scenarios. Through 100 iterations of simulations, we meticulously assess the impact of noise levels on authentication efficacy. Our results notably highlight CRYSTALS-DILITHIUM’s consistent outperformance of RAINBOW, with signature overheads of approximately 0.5% for the QKD-BB84 protocol and 0.4% for the QKD-SARG04 one, when the quantum bit error rate (QBER) is augmented up to 8%. Moreover, our study unveils a correlation between higher security levels and increased authentication times, with CRYSTALS-DILITHIUM maintaining superior efficiency across all key rates up to 10,000 kb/s. These findings underscore the substantial cost and complexity reduction achieved by mono-authentication, particularly in noisy environments, paving the way for more resilient and efficient quantum communication systems. Full article
(This article belongs to the Special Issue Quantum Optics: Trends and Challenges)
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Figure 1
<p>The signature style within the BB84 protocol is characterized by several key components [<a href="#B57-entropy-26-00447" class="html-bibr">57</a>]. In terms of communication, a visual representation is provided through the use of continuous orange arrows denoting information sent via the classical channel. Conversely, dotted orange arrows signify communication through the quantum channel, emphasizing the exchange of quantum information. The PQC algorithm is used to sign the Alice and Bob message digest and the nonce under their respective private keys to generate signatures.</p>
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<p>The signature time of mono-authentication as a function of the QBER for the two distinct protocols.</p>
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<p>The overhead of the mono-authentication as a function of the QBER for two different protocols.</p>
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<p>The graph illustrates the total authentication time, encompassing both signature and verification durations, alongside the time required for error correction, across varying maximum corrected bits given in <a href="#entropy-26-00447-t003" class="html-table">Table 3</a>. These data points are presented for three distinct security levels, all under a constant QBER of 11%.</p>
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<p>The varying security bits led to the key’s rejection, correlating with the number of bits selected for correction.</p>
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<p>The plot illustrates the signature and verification times for two post-quantum algorithms, computed for the mono-authentication scheme based on the QKD-SARG04 protocol.</p>
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<p>When QKD is authenticated with the PQC CRYSTALS-DILITHIUM algorithm, the secure key rate varies with the fiber length.</p>
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24 pages, 5548 KiB  
Article
Efficient Integration of Rate-Adaptive Reconciliation with Syndrome-Based Error Estimation and Subblock Confirmation for Quantum Key Distribution
by Patcharapong Treeviriyanupab and Chun-Mei Zhang
Entropy 2024, 26(1), 53; https://doi.org/10.3390/e26010053 - 7 Jan 2024
Cited by 1 | Viewed by 1744
Abstract
An effective post-processing algorithm is essential for achieving high rates of secret key generation in quantum key distribution. This work introduces an approach to quantum key distribution post-processing by integrating the three main steps into a unified procedure: syndrome-based error estimation, rate-adaptive reconciliation, [...] Read more.
An effective post-processing algorithm is essential for achieving high rates of secret key generation in quantum key distribution. This work introduces an approach to quantum key distribution post-processing by integrating the three main steps into a unified procedure: syndrome-based error estimation, rate-adaptive reconciliation, and subblock confirmation. The proposed scheme employs low-density parity-check codes to estimate the quantum bit error rate using the syndrome information, and to optimize the channel coding rates based on the Slepian–Wolf coding scheme for the rate-adaptive method. Additionally, this scheme incorporates polynomial-based hash verification in the subblock confirmation process. The numerical results show that the syndrome-based estimation significantly enhances the accuracy and consistency of the estimated quantum bit error rate, enabling effective code rate optimization for rate-adaptive reconciliation. The unified approach, which integrates rate-adaptive reconciliation with syndrome-based estimation and subblock confirmation, exhibits superior efficiency, minimizes practical information leakage, reduces communication rounds, and guarantees convergence to the identical key. Furthermore, the simulations indicate that the secret key throughput of this approach achieves the theoretical limit in the context of a BB84 quantum key distribution system. Full article
(This article belongs to the Special Issue Quantum and Classical Physical Cryptography)
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<p>Information reconciliation protocol based on channel coding scheme.</p>
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<p>Tanner graph representation of a binary linear block code <span class="html-italic">C</span> with a parity-check matrix <b>H</b> of dimension <span class="html-italic">M</span> × <span class="html-italic">N</span>. This graph illustrates the relationship between channel coding and Slepian–Wolf coding: (<b>a</b>) Structure of the tanner graph for channel coding, where <span class="html-italic">N</span> is the number of variable nodes, <span class="html-italic">M</span> is the number of check nodes, and the channel coding rate of linear code (<span class="html-italic">R<sub>C</sub></span>) is <math display="inline"> <semantics> <mrow> <mfrac> <mrow> <mi>N</mi> <mo>−</mo> <mi>M</mi> </mrow> <mrow> <mi>N</mi> </mrow> </mfrac> </mrow> </semantics> </math>. (<b>b</b>) Structure of the Tanner graph for Slepian–Wolf coding, where <span class="html-italic">N</span> is the number of variable nodes, <span class="html-italic">M</span> is the number of syndrome nodes, and the compression rate of syndrome (<span class="html-italic">R<sub>S</sub></span>) is <math display="inline"> <semantics> <mrow> <mfrac> <mrow> <mo> </mo> <mi>M</mi> </mrow> <mrow> <mi>N</mi> </mrow> </mfrac> </mrow> </semantics> </math>.</p>
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<p>Flowchart of the unified procedure for syndrome-based error estimation, rate-adaptive information reconciliation, and subblock confirmation using polynomial hashing.</p>
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<p>Comparison of QBER estimation methods: random key sampling with 5% and 10% sampling rates from the sifted keys and the syndrome estimation using a block length of <span class="html-italic">N</span> = 64,800 bits with <math display="inline"> <semantics> <mrow> <msubsup> <mrow> <mi>R</mi> </mrow> <mrow> <mi>C</mi> </mrow> <mrow> <mo>(</mo> <mi mathvariant="italic">max</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </semantics> </math> = 9/10 and <math display="inline"> <semantics> <mrow> <msub> <mrow> <mi>N</mi> </mrow> <mrow> <mi mathvariant="italic">sb</mi> </mrow> </msub> </mrow> </semantics> </math> = 16,200 bits with <math display="inline"> <semantics> <mrow> <msubsup> <mrow> <mi>R</mi> </mrow> <mrow> <mi>C</mi> </mrow> <mrow> <mo>(</mo> <mi mathvariant="italic">max</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </semantics> </math> = 8/9. These results are presented using box plots at four distinct observed QBER values: (<b>a</b>) 2%, (<b>b</b>) 4%, (<b>c</b>) 7%, and (<b>d</b>) 10%. For each observed QBER value, the results of all QBER estimation methods were derived from 2000 iterations.</p>
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<p>Comparison of various QBER estimation methods in terms of the mean accuracy (%) and the mean squared error (MSE) of estimated QBER (<span class="html-italic">q<sub>est</sub></span>) from 2000 iterations. The comparison of QBER estimation methods encompasses random key sampling with 5% and 10% sampling rates, as well as the syndrome estimation with a block length of <span class="html-italic">N</span> = 64,800 bits and <math display="inline"> <semantics> <mrow> <msub> <mrow> <mi>N</mi> </mrow> <mrow> <mi mathvariant="italic">sb</mi> </mrow> </msub> </mrow> </semantics> </math> = 16,200 bits. These results are obtained from simulations over three observed QBER ranges: (<b>a</b>) low error rates of 1.00–3.50%, (<b>b</b>) middle error rates of 3.51–7.00%, and (<b>c</b>) high error rates of 7.01–11%.</p>
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<p>Performance comparison of (<b>a</b>) the number of information leakages (<span class="html-italic">L<sub>rec</sub></span>), represented as a percentage; (<b>b</b>) the efficiency metric of information reconciliation ( <math display="inline"> <semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi mathvariant="italic">IR</mi> </mrow> </msub> </mrow> </semantics> </math>); and (<b>c</b>) the number of communication rounds during the information reconciliation step. In these simulations, the proposed rate-adaptive reconciliation with syndrome-based QBER estimation and subblock confirmation is evaluated and compared to other methods, including Cascade, blind, and symmetric blind. The simulation results are obtained from an average of 2000 iterations for every observed QBER point.</p>
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<p>Comparison of (<b>a</b>) the success rate (%) and (<b>b</b>) the frame error rate (FER) between the proposed rate-adaptive reconciliation performed solely in the primary round, and its integration with subblock confirmation through an iterative process in the additional rounds. These simulation results are obtained from 2000 iterations for every observed QBER value.</p>
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<p>Comparison of (<b>a</b>) the secret key rate as a function of the quantum bit error rate (QBER) and (<b>b</b>) the secret key throughput as a function of the distance over the quantum channel (km) with a QKD system operating at 1 GHz clock rate, utilizing the parameters of a BB84 QKD system as defined in <a href="#entropy-26-00053-t004" class="html-table">Table 4</a>. In these simulations, the proposed rate-adaptive reconciliation with syndrome-based estimation and subblock confirmation is evaluated and compared with Cascade, blind, and symmetric blind reconciliation.</p>
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13 pages, 6525 KiB  
Article
Quantum Communications Feasibility Tests over a UK-Ireland 224 km Undersea Link
by Ben Amies-King, Karolina P. Schatz, Haofan Duan, Ayan Biswas, Jack Bailey, Adrian Felvinti, Jaimes Winward, Mike Dixon, Mariella Minder, Rupesh Kumar, Sophie Albosh and Marco Lucamarini
Entropy 2023, 25(12), 1572; https://doi.org/10.3390/e25121572 - 22 Nov 2023
Cited by 3 | Viewed by 1714
Abstract
The future quantum internet will leverage existing communication infrastructures, including deployed optical fibre networks, to enable novel applications that outperform current information technology. In this scenario, we perform a feasibility study of quantum communications over an industrial 224 km submarine optical fibre link [...] Read more.
The future quantum internet will leverage existing communication infrastructures, including deployed optical fibre networks, to enable novel applications that outperform current information technology. In this scenario, we perform a feasibility study of quantum communications over an industrial 224 km submarine optical fibre link deployed between Southport in the United Kingdom (UK) and Portrane in the Republic of Ireland (IE). With a characterisation of phase drift, polarisation stability and the arrival time of entangled photons, we demonstrate the suitability of the link to enable international UK–IE quantum communications for the first time. Full article
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<p>Field trial and experimental setup. (<b>a</b>) Geographic representation and (<b>b</b>) satellite image of the field trial. The ‘Rockabill’ link deployed by the company euNetworks [<a href="#B33-entropy-25-01572" class="html-bibr">33</a>] is drawn as an orange line with endpoints in the cable landing stations (CLSs) of Portrane, IE, and Southport, UK. The blue dot in the top panel denotes the University of York (UoY). The whole experimental setup and its subsystems, including the SNSPDs, were moved from the UoY to the two CLSs to perform the feasibility tests. (<b>c</b>–<b>e</b>) Subsystems of the experimental setup to characterise the optical phase (top), polarisation (middle), and entangled photon pair distribution (bottom) across the UK–IE link. Map data courtesy of GHSSG, Esri, Maxar, Earthstar Geographics, and the GIS User Community.</p>
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<p>Relative phase drift of the fibre pair 39 and 40 of the Rockabill link: (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>0.5</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> of the phase drift of the channel; and (<b>b</b>) power spectral density (PSD) of the phase noise of the channel (blue), with detector noise (orange) plotted for comparison.</p>
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<p>The long-term polarisation drift of the channel over 14 <math display="inline"><semantics> <mi mathvariant="normal">h</mi> </semantics></math> overnight.</p>
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<p>Total count rates (blue) and QBER (red) for different quantum states prepared in Portrane, as measured in Southport. Plots (<b>a</b>,<b>c</b>,<b>e</b>,<b>g</b>) correspond to a preparation of the state <math display="inline"><semantics> <mrow> <mo>|</mo> <mi>H</mi> <mo>〉</mo> </mrow> </semantics></math> measured in the rectilinear basis <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>/</mo> <mi>V</mi> </mrow> </semantics></math>; plots (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>) are similar, but for the state <math display="inline"><semantics> <mrow> <mo>|</mo> <mi>V</mi> <mo>〉</mo> </mrow> </semantics></math>. Plots (<b>i</b>,<b>j</b>) correspond to the states <span class="html-italic">D</span> and <span class="html-italic">A</span> prepared, respectively, measured in the rectilinear basis <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>/</mo> <mi>V</mi> </mrow> </semantics></math>. The first and last columns were generated with photon flux <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, whereas columns 2–4 depict the states at <math display="inline"><semantics> <mi>μ</mi> </semantics></math> equal to 0.6, 0.5, and 0.4, respectively.</p>
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<p>Simulation of the secret key rate (SKR, blue solid line) with the parameters of the UK–IE field trial (inset) and our experimental point (orange empty diamond). The distance of the field trial between Alice, in the Portrane CLS, and Bob, in the Southport CLS, is 224 km, which is only 9 km shorter than the maximum distance providing a positive SKR (233 km). Parameters—<math display="inline"><semantics> <msub> <mi>η</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </semantics></math>: detection efficiency (SNSPD); <math display="inline"><semantics> <msub> <mi>η</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> </semantics></math>: efficiency of the receiver; <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mi>d</mi> <mi>a</mi> <mi>r</mi> <mi>k</mi> </mrow> </msub> </semantics></math>: dark counts; <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>y</mi> </mrow> </msub> </semantics></math>: background photons from the channel; <math display="inline"><semantics> <msub> <mi>e</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </semantics></math>: optical noise; <math display="inline"><semantics> <mi>μ</mi> </semantics></math>: mean photon number; <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>c</mi> <mi>l</mi> <mi>o</mi> <mi>c</mi> <mi>k</mi> </mrow> </msub> </semantics></math>: clock rate of the simulated system.</p>
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<p>Histogram of the time delays between consecutive photon detections at the end of the two submarine channels. Pair photons from the EPS arrive with a fixed relative delay of 113 <math display="inline"><semantics> <mi mathvariant="normal">n</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> at a signal-to-noise ratio of 1.92, computed over the indicated red 12 <math display="inline"><semantics> <mi mathvariant="normal">n</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> coincidence window. The green lines indicates an exemplary coincidence window including only accidentals. The inlay shows the typical spectrum of the stray photon noise present in the channel, with the dashed lines indicating the wavelengths chosen for the EPS measurement.</p>
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7 pages, 1225 KiB  
Article
Experimental Demonstration of Secure Relay in Quantum Secure Direct Communication Network
by Min Wang, Wei Zhang, Jianxing Guo, Xiaotian Song and Guilu Long
Entropy 2023, 25(11), 1548; https://doi.org/10.3390/e25111548 - 16 Nov 2023
Cited by 3 | Viewed by 1441
Abstract
Quantum secure direct communication (QSDC) offers a practical way to realize a quantum network which can transmit information securely and reliably. Practical quantum networks are hindered by the unavailability of quantum relays. To overcome this limitation, a proposal has been made to transmit [...] Read more.
Quantum secure direct communication (QSDC) offers a practical way to realize a quantum network which can transmit information securely and reliably. Practical quantum networks are hindered by the unavailability of quantum relays. To overcome this limitation, a proposal has been made to transmit the messages encrypted with classical cryptography, such as post-quantum algorithms, between intermediate nodes of the network, where encrypted messages in quantum states are read out in classical bits, and sent to the next node using QSDC. In this paper, we report a real-time demonstration of a computationally secure relay for a quantum secure direct communication network. We have chosen CRYSTALS-KYBER which has been standardized by the National Institute of Standards and Technology to encrypt the messages for transmission of the QSDC system. The quantum bit error rate of the relay system is typically below the security threshold. Our relay can support a QSDC communication rate of 2.5 kb/s within a 4 ms time delay. The experimental demonstration shows the feasibility of constructing a large-scale quantum network in the near future. Full article
(This article belongs to the Special Issue New Advances in Quantum Communication and Networks)
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<p>The architecture of QSDC network with computationally secure relay. The orange line denotes the classical channel. The green line denotes the quantum channel. PQC: post-quantum cryptography; Q-T: quantum transmitter; Q-R: quantum receiver.</p>
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<p>The architecture of the computationally secure relay. Rec.: receiver; Rconsys: receiver control system; Trans.: transmitter; Tconsys: transmitter control system; LDPC-H: low-density parity check and Hadamard code.</p>
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<p>Experimental setup of the QSDC network with a computationally secure relay. Alice encrypts the message and sends the ciphertext to the relay through the quantum channel. Bob receives the signals from the relay and decrypts the message after implementing the QSDC protocol. KYBER makes use of two hash functions H (SHA3-256) and G (SHA3-512) and a key derivation function KDF (SHAKE-256) in the realization. AMZI: asymmetric Mach–Zehnder interferometer; Attn: attenuator; PC: polarization controller; PM: phase modulator; BS: beam splitter; PBS: polarization beam splitter; CIR: circulator; FR: Faraday rotator; SPD: single-photon detector.</p>
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<p>Delay time at the relay.</p>
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<p>Communication rate of the relayed QSDC system. Communication rate (<b>a</b>) from Alice to relay; (<b>b</b>) from relay to Bob. Insets are the typical QBER of the QSDC system.</p>
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15 pages, 597 KiB  
Article
Quantum Honeypots
by Naya Nagy, Marius Nagy, Ghadeer Alazman, Zahra Hawaidi, Saja Mustafa Alsulaibikh, Layla Alabbad, Sadeem Alfaleh and Areej Aljuaid
Entropy 2023, 25(10), 1461; https://doi.org/10.3390/e25101461 - 18 Oct 2023
Cited by 1 | Viewed by 1455
Abstract
Quantum computation offers unique properties that cannot be paralleled by conventional computers. In particular, reading qubits may change their state and thus signal the presence of an intruder. This paper develops a proof-of-concept for a quantum honeypot that allows the detection of intruders [...] Read more.
Quantum computation offers unique properties that cannot be paralleled by conventional computers. In particular, reading qubits may change their state and thus signal the presence of an intruder. This paper develops a proof-of-concept for a quantum honeypot that allows the detection of intruders on reading. The idea is to place quantum sentinels within all resources offered within the honeypot. Additional to classical honeypots, honeypots with quantum sentinels can trace the reading activity of the intruder within any resource. Sentinels can be set to be either visible and accessible to the intruder or hidden and unknown to intruders. Catching the intruder using quantum sentinels has a low theoretical probability per sentinel, but the probability can be increased arbitrarily higher by adding more sentinels. The main contributions of this paper are that the monitoring of the intruder can be carried out at the level of the information unit, such as the bit, and quantum monitoring activity is fully hidden from the intruder. Practical experiments, as performed in this research, show that the error rate of quantum computers has to be considerably reduced before implementations of this concept are feasible. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
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<p>The hidden sentinel is the second qubit in the figure. It is acted on by the datum sentinel via the control of phase shift gates. The middle of the figure shows the area and time when the datum-qubit is exposed to the user.</p>
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<p>The legal user measures the sentinels in the correct bases.</p>
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<p>The measurement probability of <a href="#entropy-25-01461-f002" class="html-fig">Figure 2</a>, which has four sentinels, and the user is legal.</p>
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<p>Experiment with four positional sentinels. The intruder’s behavior is random, as the state of the sentinels is not known to the user. In this particular case, the intruder makes a mistake on <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math> and, therefore, the detection probability is theoretically <math display="inline"><semantics> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </semantics></math>.</p>
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<p>The measurement probability of <a href="#entropy-25-01461-f004" class="html-fig">Figure 4</a>, which contains four positional sentinels, and the intruder misses one.</p>
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<p>Four positional sentinels are set to all possible values. The experiment shows the option where the intruder is lucky on only one qubit, namely <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>The measurement probability of <a href="#entropy-25-01461-f006" class="html-fig">Figure 6</a> with four positional sentinels and the intruder missing three of the sentinels. The result in red refers to the probability of the intruder to escape detection.</p>
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<p>Legal user reading a datum qubit with a hidden sentinel. The same circuit applies to a lucky intruder. The user does not disturb the state of the datum qubit.</p>
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<p>Unlucky intruder reading a quantum qubit with a hidden sentinel. In the case of an unlucky intruder, an extra Hadamard gate on the datum qubit disturbs the hidden sentinel.</p>
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<p>The circuit with two active hidden sentinels shows an intruder that has wrongly measured two datum qubits, <math display="inline"><semantics> <msub> <mi>q</mi> <mn>0</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math>, that act on two hidden sentinels, <math display="inline"><semantics> <msub> <mi>q</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>q</mi> <mn>3</mn> </msub> </semantics></math>.</p>
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<p>The left panel shows the practical results obtained on running a circuit with two hidden sentinels. The panel on the right shows the theoretical expectation.</p>
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10 pages, 1458 KiB  
Article
Practical Real-Time Phase Drift Compensation Scheme for Quantum Communication Systems
by Xiaotian Song, Chunsheng Zhang, Dong Pan, Min Wang, Jianxing Guo, Feihao Zhang and Guilu Long
Entropy 2023, 25(10), 1408; https://doi.org/10.3390/e25101408 - 1 Oct 2023
Cited by 2 | Viewed by 1299
Abstract
Quantum communication systems are susceptible to various perturbations and drifts arising from the operational environment, with phase drift being a crucial challenge. In this paper, we propose an efficient real-time phase drift compensation scheme in which only existing data from the quantum communication [...] Read more.
Quantum communication systems are susceptible to various perturbations and drifts arising from the operational environment, with phase drift being a crucial challenge. In this paper, we propose an efficient real-time phase drift compensation scheme in which only existing data from the quantum communication process is used to establish a stable closed-loop control subsystem for phase tracking. This scheme ensures the continuous operation of transmission by tracking and compensating for phase drift in the phase-encoding quantum communication system. The experimental results demonstrate the effectiveness and feasibility of the proposed scheme with an average quantum bit error rate of 1.60% and a standard deviation of 0.0583% for 16 h of continuous operation. Full article
(This article belongs to the Special Issue New Advances in Quantum Communication and Networks)
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<p>The main flowchart of the real-time phase drift compensation scheme. Calc, the calculation module to calculate the incremental driving voltage <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>V</mi> <mi>i</mi> </msub> </mrow> </semantics></math> using the initial parameters and <math display="inline"><semantics> <msub> <mi>e</mi> <mi>i</mi> </msub> </semantics></math>; P, I, and D respectively represent the proportional, integral, and derivative components; ∑, sum of the three components.</p>
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<p>Schematic of the experimental setup. IM, intensity modulator; FSMI, asymmetric Faraday–Sagnac–Michelson interferometer; BS, beam splitter; FM, Faraday mirror; PBS, polarization beam splitter; FR, Faraday rotator; PM, phase modulator; ATT, attenuator; CIR, circulator; SPD, single-photon detector. The yellow lines represent polarization-maintaining fibers (PMFs), and the blue ones are single-mode fibers (SMFs).</p>
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<p>QBER verse Driving Voltage of the phase modulator.</p>
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<p>Obtained QBER (<b>a</b>) and driving voltage of the phase modulator (<b>b</b>) with a feedback compensation frequency of 1 s per iteration.</p>
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<p>Obtained QBER (<b>a</b>) and driving voltage of the phase modulator (<b>b</b>) with a feedback compensation frequency of 0.1 s per iteration.</p>
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<p>QBER, its statistical distribution (<b>a</b>), and driving voltage of the phase modulator (<b>b</b>) with a feedback compensation frequency of 0.1 s per iteration for 16 h.</p>
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21 pages, 7944 KiB  
Article
Uplink and Downlink NOMA Based on a Novel Interference Coefficient Estimation Strategy for Next-Generation Optical Wireless Networks
by Syed Agha Hassnain Mohsan, Yanlong Li, Zejun Zhang, Amjad Ali and Jing Xu
Photonics 2023, 10(5), 569; https://doi.org/10.3390/photonics10050569 - 12 May 2023
Cited by 1 | Viewed by 2490
Abstract
Non-orthogonal multiple access (NOMA) has been widely recognized as a promising technology to improve the transmission capacity of wireless optical communication systems. NOMA considers the principle of successive interference cancellation (SIC) to separate a user’s signal at the receiver side. To improve the [...] Read more.
Non-orthogonal multiple access (NOMA) has been widely recognized as a promising technology to improve the transmission capacity of wireless optical communication systems. NOMA considers the principle of successive interference cancellation (SIC) to separate a user’s signal at the receiver side. To improve the ability of optical signal detection, we developed a quantum dot (QD) fluorescent concentrator incorporated with multiple-input and single-output (MISO) to realize an uplink NOMA-based optical wireless system. However, inaccurate interference assessment of multiple users using the SIC detection algorithm at the receiver side may lead to more prominent error propagation problems and affect the bit error rate (BER) performance of the system. This research aims to propose a novel recurrent neural network-based guided frequency interference coefficient estimation algorithm in a NOMA visible light communication (VLC) system. This algorithm can improve the accuracy of interference estimation compared with the traditional SIC detection algorithm by introducing interference coefficients. It provides a more accurate reconstruction possibility for level-by-level interference cancellation and weakens the influence of error propagation. In addition, we designed uplink and downlink NOMA-VLC communication systems for experimental validation. When the power allocation ratio was in the range of 0.8 to 0.97, the experimental results of the downlink validated that the BER performance of both users satisfied the forward error correction (FEC) limit with the least squares (LS)-SIC and the long short-term memory recurrent neural networks (LSTM)-SIC detection strategy. Moreover, the BER performance of the LSTM-SIC algorithm was better than that of the LS-SIC algorithm for all users when the power allocation ratio was in the range of 0.92 to 0.93. In particular, our proposed system offered a large detection area of 2 cm2 and corresponding aggregate data rate up to 40 Mbps over 1.5 m of free space by using QDs, and we successfully achieved a mean bit error rate (BER) of 2.3 × 10−3 for the two users. Full article
(This article belongs to the Special Issue Underwater Wireless Optical Communication, Sensor and Network)
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<p>Indoor optical communication scene diagram.</p>
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<p>Material-1: (<b>a</b>) normalized excitation spectra of QDs, (<b>b</b>) normalized emission spectra of QDs, (<b>c</b>) TEM, and (<b>d</b>) high-resolution TEM images of the QD material.</p>
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<p>Material-2: (<b>a</b>) normalized excitation spectra of QDs, (<b>b</b>) normalized emission spectra of QDs, (<b>c</b>) TEM, and (<b>d</b>) high-resolution TEM images of the QD material.</p>
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<p>Downlink 2-user NOMA capacity region.</p>
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<p>SIC schematic block diagram.</p>
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<p>Four interacting neural network layers in the repetition module of the LSTM.</p>
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<p>Prediction results of training of interference coefficient.</p>
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<p>Blocks diagrams of the experimental setup: (<b>a</b>) block diagram of downlink NOMA-VLC using LSTM SIC receivers; (<b>b</b>) block diagram of uplink NOMA-VLC using quantum dots.</p>
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<p>P–I and V–I measurement results.</p>
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<p>BER performance of NOMA-VLC under different bias current values.</p>
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<p>BER performance of NOMA-VLC under different attenuation values.</p>
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<p>BER performance of two users with Material-2 for various power allocation ratios.</p>
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<p>Original BER curve without interference estimation optimization.</p>
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<p>BERs at different distances with interference estimation optimization. Insets: eye diagrams of (<b>a</b>) the first user with equalization, (<b>b</b>) the second user with equalization, (<b>c</b>) the second user with LS-SIC, and (<b>d</b>) the second user with LSTM-SIC.</p>
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<p>BERs under different power allocation ratios with interference estimation optimization.</p>
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<p>BERs at optimal power allocation ratio of 0.91 with interference estimation optimization.</p>
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<p>BERs at optimal power allocation ratio of 0.92 with interference estimation optimization.</p>
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<p>BERs at optimal power allocation ratio of 0.93 with interference estimation optimization.</p>
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7 pages, 686 KiB  
Communication
Optimized Polarization Encoder with High Extinction Ratio for Quantum Key Distribution System
by Pengcheng Wang, Qianqian Zhang, Huanwen Xie and Banghong Guo
Electronics 2023, 12(8), 1859; https://doi.org/10.3390/electronics12081859 - 14 Apr 2023
Viewed by 1822
Abstract
Polarization encoding is a promising approach for practical quantum key distribution (QKD) systems due to its simple encoding and decoding methodology. In this study, we propose a self-compensating polarization encoder (SCPE) based on a phase modulator, which can be composed of commercial off-the-shelf [...] Read more.
Polarization encoding is a promising approach for practical quantum key distribution (QKD) systems due to its simple encoding and decoding methodology. In this study, we propose a self-compensating polarization encoder (SCPE) based on a phase modulator, which can be composed of commercial off-the-shelf (COT) devices. We conducted a proof-of-concept experiment to test the SCPE, which demonstrated an in-system quantum bit error rate (QBER) of 0.53% and long-term running stability without any active adjustments. Additionally, we conducted experiments with transmission over commercial fiber spools of lengths up to 100 km and obtained a secure finite key rate of 3 kbps. Our polarization encoder is a promising solution for various polarization encoding protocols, including BB84, MDI, and RFI. Full article
(This article belongs to the Special Issue Quantum Information, Computation and Cryptography)
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<p>Schematic and experimental diagram of the QKD system. (<b>a</b>) Schematic diagram of SCPE LD, laser diode (Qasky Co. Ltd., Wuhu, China); Circ, circulators; PC, polarization controller; PBS, polarized beam splitter; PM, phase modulator (China Electronics Technology Group Co. Ltd., Chongqing, China); FR, Faraday rotator; VOA, variable optical attenuator; D1–D4, single-photon detector (Langyan Optoelectronic Technology Co. Ltd., Shanghai, China). (<b>b</b>) Experimental setup of the QKD system.</p>
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<p>Measured QBERs of four polarization states of <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mi>H</mi> <mo>〉</mo> </mrow> <mo>,</mo> <mrow> <mo>|</mo> <mi>V</mi> <mo>〉</mo> </mrow> <mo>,</mo> <mrow> <mo>|</mo> <mi>D</mi> <mo>〉</mo> </mrow> <mo>,</mo> <mrow> <mo>|</mo> <mi>A</mi> <mo>〉</mo> </mrow> </mrow> </semantics></math>, and 20 km and 50 km commercial optical fiber for 30 min, demonstrating stability.</p>
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<p>The key rate performance of SCPE. The experimental rate distance performance of SCPE, compared with the theoretical simulations, along with Peng [<a href="#B35-electronics-12-01859" class="html-bibr">35</a>] and Ma [<a href="#B32-electronics-12-01859" class="html-bibr">32</a>].</p>
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17 pages, 973 KiB  
Article
Reverse Reconciliation for Optimal Error Correction in Quantum Key Distribution
by Luis Adrián Lizama-Perez
Symmetry 2023, 15(3), 710; https://doi.org/10.3390/sym15030710 - 12 Mar 2023
Cited by 4 | Viewed by 1777
Abstract
In this work, we introduce a new method for the establishment of a symmetric secret key through the reconciliation process in QKD systems that, we claim, is immune to the error rate of the quantum channel and, therefore, has an efficiency of 100% [...] Read more.
In this work, we introduce a new method for the establishment of a symmetric secret key through the reconciliation process in QKD systems that, we claim, is immune to the error rate of the quantum channel and, therefore, has an efficiency of 100% since it does not present losses during the distillation of secret keys. Furthermore, the secret rate is scaled to the square of the number of pulses on the destination side. The method only requires a single data exchange from Bob over the classic channel. We affirmed that our results constitute a milestone in the field of QKD and error correction methods at a crucial moment in the development of classical and quantum cryptanalytic algorithms. We believe that the properties of our method can be evaluated directly since it does not require the use of complex formal-theoretical techniques. For this purpose, we provide a detailed description of the reconciliation algorithm. The strength of the method against PNS and IR attacks is discussed. Furthermore, we define a method to analyze the security of the reconciliation approach based on frames that are binary arrays of 2×2. As a result, we came to the conclusion that the conjugate approach can no longer be considered secure, while we came up with a way to increase the secret gain of the method with measured bits. Full article
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<p>The quantum states of the BB84 protocol and the two measurement bases <math display="inline"><semantics> <mi mathvariant="bold">X</mi> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="bold">Z</mi> </semantics></math> are represented through the bi-dimensional Bloch sphere. A bit is encoded by means of a pair of non-orthogonal states.</p>
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<p>The pairs of quantum states are separated as orthogonal, non-orthogonal, and parallel states.</p>
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<p>The diagram shows the sifting strings (SSs) for the different instances at Bob’s side, which are represented as SS<math display="inline"><semantics> <msub> <mrow/> <mi>i</mi> </msub> </semantics></math> labels with <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>10</mn> </mrow> </semantics></math>. The resulting labels depend on the specific approach that is used, and they are shown in <a href="#symmetry-15-00710-t001" class="html-table">Table 1</a>.</p>
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<p>General QKD protocol based on XOR bits. The final step is for Alice and Bob to confirm that they have both set the same secret key because Alice sends the hash code of the distilled key to Bob and obtains a positive confirmation from him.</p>
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<p>An example of the labels contained in the lists <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>=</mo> <mrow> <mo stretchy="false">{</mo> <mrow> <mo>[</mo> <msub> <mi>ϵ</mi> <mn>11</mn> </msub> <mo>,</mo> <msub> <mi>ϵ</mi> <mn>12</mn> </msub> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <msub> <mi>π</mi> <mn>11</mn> </msub> <mo>,</mo> <msub> <mi>π</mi> <mn>12</mn> </msub> <mo>]</mo> </mrow> <mo stretchy="false">}</mo> </mrow> <mo>,</mo> <mrow> <mo stretchy="false">{</mo> <mrow> <mo>[</mo> <msub> <mi>π</mi> <mn>21</mn> </msub> <mo>,</mo> <msub> <mi>π</mi> <mn>22</mn> </msub> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <msub> <mi>ϵ</mi> <mn>21</mn> </msub> <mo>,</mo> <msub> <mi>ϵ</mi> <mn>22</mn> </msub> <mo>]</mo> </mrow> <mo stretchy="false">}</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mo stretchy="false">{</mo> <mrow> <mo>[</mo> <msub> <mi>ϵ</mi> <mn>11</mn> </msub> <mo>,</mo> <msub> <mi>ϵ</mi> <mn>12</mn> </msub> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <msub> <mi>ϵ</mi> <mn>21</mn> </msub> <mo>,</mo> <msub> <mi>ϵ</mi> <mn>22</mn> </msub> <mo>]</mo> </mrow> <mo stretchy="false">}</mo> </mrow> <mo>,</mo> <mrow> <mo stretchy="false">{</mo> <mrow> <mo>[</mo> <msub> <mi>π</mi> <mn>11</mn> </msub> <mo>,</mo> <msub> <mi>π</mi> <mn>12</mn> </msub> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <msub> <mi>π</mi> <mn>21</mn> </msub> <mo>,</mo> <msub> <mi>π</mi> <mn>22</mn> </msub> <mo>]</mo> </mrow> <mo stretchy="false">}</mo> </mrow> </mrow> </semantics></math>. At the bottom of each frame, we have written the XOR bits.</p>
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<p>There are four configurations for T.1: the inputs are written in the left-hand corners (<b>top</b>, <b>bottom</b>), while the test cases appear in the right-hand corners. The implicit SSs are written above the arrows. The (<b>c</b>,<b>d</b>) configurations are just the reflection of the (<b>a</b>,<b>b</b>) ones, respectively.</p>
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8 pages, 1628 KiB  
Communication
Combined Optical Fiber Transmission System Based on QNSC and BER-LM
by Xiaokun Yang, Xiangqing Wang, Dongfei Wang, Lan Zhang, Zufang Yang, Han Zhu and Baohong Wu
Photonics 2023, 10(2), 154; https://doi.org/10.3390/photonics10020154 - 2 Feb 2023
Cited by 1 | Viewed by 1455
Abstract
A quantum noise stream cipher (QNSC) is a physical layer encryption technology based on quantum noise. Bit error rate loopback measurement (BER-LM) is a method to measure the BER of a loopback channel and extract channel characteristics. Then, channel characteristics can be extracted, [...] Read more.
A quantum noise stream cipher (QNSC) is a physical layer encryption technology based on quantum noise. Bit error rate loopback measurement (BER-LM) is a method to measure the BER of a loopback channel and extract channel characteristics. Then, channel characteristics can be extracted, and consensus keys can be obtained through negotiation. In previous studies, encryption and key distribution were implemented in independent channels. In this paper, we propose a scheme that combines these two technologies in a single fiber channel to achieve encrypted transmission and key distribution. We verified a 20 Gbps QPSK coherent optical transmission system with a PSK/QNSC scheme. The results show that by reasonably setting the negotiation bit position, the consensus key could be obtained through negotiation, and the requirements of transmission performance could be met. When the negotiation bit position was set to seven, the Q-factor of the system was nine, which met the error-free condition of the 7% forward error correction (FEC) limit. Full article
(This article belongs to the Special Issue Optical Fiber Transmission Systems)
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<p>A 2PSK signal encryption procedure with a PSK/QNSC scheme.</p>
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<p>BER of loopback fiber channel measured by Alice and Bob.</p>
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<p>(<b>a</b>) Encryption transmission principle of optical fiber communication. (<b>b</b>) Principle of transmission and negotiation integrated transformation.</p>
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<p>System schematic diagram of QNSC and BER-LM.</p>
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<p>The specific operation steps of QNSC and BER-LM.</p>
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<p>(<b>a</b>) System device diagram of loopback optical fiber channel. (<b>b</b>) Received PSK/QNSC signal and decrypted QPSK signal.</p>
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<p>(<b>a</b>) Q-factor vs. distance for PSK/QNSC and regular QPSK without PSK/QNSC. (<b>b</b>) DFP vs. OSNR for Eve at different OSNR values with encrypted signals of 220PSK, 218PSK, and 216PSK.</p>
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<p>BER measured by Alice, Bob, and Eve at different time points.</p>
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<p>(<b>a</b>) Q-factor vs. bit position. (<b>b</b>) BER measured by Bob and Eve at different bit positions.</p>
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13 pages, 405 KiB  
Communication
Security of Bennett–Brassard 1984 Quantum-Key Distribution under a Collective-Rotation Noise Channel
by Mhlambululi Mafu, Comfort Sekga and Makhamisa Senekane
Photonics 2022, 9(12), 941; https://doi.org/10.3390/photonics9120941 - 6 Dec 2022
Cited by 4 | Viewed by 1760
Abstract
The security analysis of the Ekert 1991 (E91), Bennett 1992 (B92), six-state protocol, Scarani–Acín–Ribordy–Gisin 2004 (SARG04) quantum key distribution (QKD) protocols, and their variants have been studied in the presence of collective-rotation noise channels. However, besides the Bennett–Brassard 1984 (BB84) being the first [...] Read more.
The security analysis of the Ekert 1991 (E91), Bennett 1992 (B92), six-state protocol, Scarani–Acín–Ribordy–Gisin 2004 (SARG04) quantum key distribution (QKD) protocols, and their variants have been studied in the presence of collective-rotation noise channels. However, besides the Bennett–Brassard 1984 (BB84) being the first proposed, extensively studied, and essential protocol, its security proof under collective-rotation noise is still missing. Thus, we aim to close this gap in the literature. Consequently, we investigate how collective-rotation noise channels affect the security of the BB84 protocol. Mainly, we study scenarios where the eavesdropper, Eve, conducts an intercept-resend attack on the transmitted photons sent via a quantum communication channel shared by Alice and Bob. Notably, we distinguish the impact of collective-rotation noise and that of the eavesdropper. To achieve this, we provide rigorous, yet straightforward numerical calculations. First, we derive a model for the collective-rotation noise for the BB84 protocol and parametrize the mutual information shared between Alice and Eve. This is followed by deriving the quantum bit error rate (QBER) for two intercept-resend attack scenarios. In particular, we demonstrate that, for small rotation angles, one can extract a secure secret key under a collective-rotation noise channel when there is no eavesdropping. We observe that noise induced by rotation of 0.35 radians of the prepared quantum state results in a QBER of 11%, which corresponds to the lower bound on the tolerable error rate for the BB84 QKD protocol against general attacks. Moreover, a rotational angle of 0.53 radians yields a 25% QBER, which corresponds to the error rate bound due to the intercept-resend attack. Finally, we conclude that the BB84 protocol is robust against intercept-resend attacks on collective-rotation noise channels when the rotation angle is varied arbitrarily within particular bounds. Full article
(This article belongs to the Section Optical Communication and Network)
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<p>An illustration of the two intercept-and-resend attack strategies. The quantum channel is denoted by straight arrows, while dashed arrows depict lossless classical channels. (<b>a</b>) Eve breaks the quantum channel between Alice and Bob and places her devices between the two parties. (<b>b</b>) Eve places her preparation device at a location close to, possibly inside, Bob’s lab and connects her measurement and preparation devices by a lossless classical channel. The letters P and M represent preparation and measurement devices, respectively.</p>
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<p>Comparison of the variation of the quantum bit error rate <span class="html-italic">Q</span> with the rotation angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> for the case where there is no eavesdropping (<math display="inline"><semantics> <msub> <mi>Q</mi> <mn>0</mn> </msub> </semantics></math>), the case where the eavesdropper performs the attack outlined in the strategy shown in <a href="#photonics-09-00941-f001" class="html-fig">Figure 1</a>a (<math display="inline"><semantics> <msub> <mi>Q</mi> <mn>1</mn> </msub> </semantics></math>), and the case where the eavesdropper performs the attack outlined in the strategy shown in <a href="#photonics-09-00941-f001" class="html-fig">Figure 1</a>b (<math display="inline"><semantics> <msub> <mi>Q</mi> <mn>2</mn> </msub> </semantics></math>).</p>
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<p>Variation of the mutual information between Alice and Eve <span class="html-italic">I(A:E)</span> as a function of the collective-rotation noise <math display="inline"><semantics> <mi>ε</mi> </semantics></math>.</p>
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18 pages, 1599 KiB  
Article
Quantum-Chromodynamics-Inspired 2D Multicolor LED Matrix to Camera Communication for User-Centric MIMO
by Geetha Vasantha and Sanket Salvi
Appl. Sci. 2022, 12(20), 10204; https://doi.org/10.3390/app122010204 - 11 Oct 2022
Cited by 1 | Viewed by 1975
Abstract
With the high availability of low-cost and energy-efficient LEDs and cameras, there is increased interest in optical camera communication (OCC) to provide nonradio-frequency-based communication solutions in the domains of advertisement, vehicular communication, and the Internet of Things (IoT). As per the IEEE 802.15.7-2018 [...] Read more.
With the high availability of low-cost and energy-efficient LEDs and cameras, there is increased interest in optical camera communication (OCC) to provide nonradio-frequency-based communication solutions in the domains of advertisement, vehicular communication, and the Internet of Things (IoT). As per the IEEE 802.15.7-2018 standard, new physical-layer clauses support low-frame-rate camera communication with allowable flickering. This paper proposes an OCC system that can provide user-centric multiple-input multiple-output (MIMO) loosely based on quantum-chromodynamics (QCD) concepts. A QCD–OCC simulator and prototype are proposed, implemented, and evaluated on the basis of the pixel intensity profile, peak signal-to-noise ratio (PSNR), the success of reception (%), bit-error rate (BER), and throughput under different ambient lighting conditions and distances. We observed 100% and 84% success of reception using the proposed prototype and simulator, respectively, for the data rate of 720 bps. The maximal tolerable BER of 1.13×102 for IoT applications was observed at a maximal distance of 200 cm and a maximal data rate of 3600 bps. The proposed system was also compared with other existing OCC systems with similar hardware and implementation requirements. The proposed QCD–OCC system provided rotation support up to 90 degrees and throughput of 4.32 kbps for a 30 fps camera. Full article
(This article belongs to the Special Issue Optical Camera Communications and Applications)
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<p>User-centric MIMO under OCC access point. (<b>a</b>) Three user devices of 1× bandwidth; (<b>b</b>) one user device of 3× bandwidth.</p>
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<p>Gluon-exchange-based color changes in quarks, baryon model.</p>
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<p>Overview of proposed QCD–OCC system.</p>
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<p>Block diagram of the proposed QCD–OCC transmitter simulator.</p>
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<p>Proposed OCC modulation scheme frame format and color channel multiplexing process.</p>
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<p>Block diagram of the proposed QCD–OCC receiver simulator.</p>
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<p>Tx and Rx simulator screenshots of proposed QCD–OCC system.</p>
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<p>Implementation of proposed Tx. (<b>a</b>) Circuit diagram; (<b>b</b>) connected hardware components.</p>
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<p>Implemented QCD–OCC prototype system.</p>
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<p>Tx intensity profile at distances L = 50, 100, and 200 cm.</p>
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<p>Comparison of success of reception (%) between implemented proposed QCD–OCC simulator and proposed QCD–OCC prototype.</p>
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<p>Evaluation of proposed prototype. (<b>a</b>) PSNR at distances 50, 100, 150, and 200 cm under different ambient lighting conditions. (<b>b</b>) Success of reception (%) at distances 50, 100, 150, and 200 cm under different ambient lighting conditions.</p>
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<p>Performance evaluation of proposed prototype. (<b>a</b>) BER vs. distance vs. Tx data rate; (<b>b</b>) data throughput of other similar systems.</p>
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