Abstract
We propose two novel schemes for controlled bidirectional remote state preparation of single- and two-qubit state by using five- and nine-qubit entangled state as the quantum channel. First, our schemes are considered in two cases that the coefficients of prepared state are real and complex, respectively. Second, by virtue of appropriate measurement and the corresponding local unitary operations, we explicitly give how to accomplish these preparation tasks. Third, taking the first scheme as an example, we discuss our scheme in four kinds of noisy environments (bit-flip, phase-flip, amplitude-damping and depolarizing noisy environment). We calculate fidelity and find that it depends on the prepared state coefficients and decoherence rate. Eventually, some discussions are given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bennett, C.H., Brassard, G., Crpeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and EinsteinCPodolskyCRosen channels. Phys. Rev. Lett. 70(1985), 13–29 (1993)
Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)
Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)
Chen, X.B., Ma, S.Y., Su, Y., Zhang, R., Yang, Y.X.: Controlled remote state preparation of arbitrary two and three qubit states via the Brown state. Q. Inf. Process. 11(6), 1653–1667 (2012)
Dakic, B.: Quantum discord as resource for remote state preparation. Nat. Phys. 8(9), 666–670 (2012)
Chen, X.B., Sun, Y.R., Xu, G., Jia, H.Y., Qu, Z., Yang, Y.X.: Controlled bidirectional remote preparation of three-qubit state. Q. Inf. Process. 16(10), 244 (2017)
Cao, T.B., Nguyen, B.A.: Deterministic controlled bidirectional remote state preparation. Adv. Nat. Sci. Nanosci. Nanotechnol. 5(1), 015003 (2013)
Sharma, V., Shukla, C., Banerjee, S., Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. Q. Inf. Process. 14(9), 3441–3464 (2015)
Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional controlled joint remote state preparation. Q. Inf. Process. 14(11), 4263–4278 (2015)
Zhang, D., Zha, X., Duan, Y., Wei, Z.H.: Deterministic controlled bidirectional remote state preparation via a six-qubit maximally entangled state. Int. J. Theor. Phys. 55(1), 440–446 (2016)
Zhang, D., Zha, X., Duan, Y., Yang, Y.: Deterministic controlled bidirectional remote state preparation via a six-qubit entangled state. Q. Inf. Process. 15(5), 2169–2179 (2016)
Li, Y., Jin, X.: Bidirectional controlled teleportation by using nine-qubit entangled state in noisy environments. Q. Inf. Process. 15(2), 929–945 (2016)
O’Brien, J.L., Pryde, G.J., White, A.G., Ralph, T.C., Branning, D.: Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264–267 (2003)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and con Tos5. In: Proceedings of the International Conference on Computers, Systems and Signal Processing (1984)
Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441 (2000)
Liang, X.T.: Classical information capacities of some single qubit quantum noisy channels. Commun. Theor. Phys. 39(5), 537–542 (2003)
Acknowledgment
This work is supported by the NSFC (Grant Nos. 61671087, 61272514, 61170272, 61003287), the Major Science and Technology Support Program of Guizhou Province (Grant No. 20183001), the Fok Ying Tong Education Foundation (Grant No. 131067), and Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (2017BDKFJJ007).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Appendix
Appendix
When the prepared state coefficients are real. Alice’s and Bob’s unitary operations are executed, respectively, where I, X, iY, Z are pauli operations.
Alice’s and Bob’s result | Charlie’s result | Unitary operation |
|---|---|---|
\(|H_{1}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{1}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{1}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{1}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{2}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{2}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{2}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{2}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{3}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{3}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{3}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{3}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{4}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{4}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{4}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{4}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{1}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{1}\rangle _{79}|K_{2}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{1}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{1}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes I_{6}\otimes Z_{8}\) |
\(|H_{2}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{2}\rangle _{79}|K_{2}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{2}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{2}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes I_{6}\otimes Z_{8}\) |
\(|H_{3}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{3}\rangle _{79}|K_{2}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{3}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{3}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes I_{6}\otimes Z_{8}\) |
\(|H_{4}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{4}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{4}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{4}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes I_{6}\otimes Z_{8}\) |
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Sun, YR., Xu, G., Chen, XB., Yang, YX. (2018). Controlled Bidirectional Remote Preparation of Single- and Two-Qubit State. In: Sun, X., Pan, Z., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2018. Lecture Notes in Computer Science(), vol 11065. Springer, Cham. https://doi.org/10.1007/978-3-030-00012-7_49
Download citation
DOI: https://doi.org/10.1007/978-3-030-00012-7_49
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00011-0
Online ISBN: 978-3-030-00012-7
eBook Packages: Computer ScienceComputer Science (R0)