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.
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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).
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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 |
|---|---|---|
\(|H_{1}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{1}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{1}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{1}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes I_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{2}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{2}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{2}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{2}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(I_{3}\otimes -iY_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{3}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{3}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{3}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{3}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -Z_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{4}\rangle _{79}|K_{1}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes I_{6}\otimes I_{8}\) |
\(|H_{4}\rangle _{79}|K_{2}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes I_{6}\otimes -iY_{8}\) |
\(|H_{4}\rangle _{79}|K_{3}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes iY_{6}\otimes -Z_{8}\) |
\(|H_{4}\rangle _{79}|K_{4}\rangle _{24}\) | \(|0\rangle _{1}\) | \(iY_{3}\otimes -X_{5}\otimes iY_{6}\otimes -X_{8}\) |
\(|H_{1}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{1}\rangle _{79}|K_{2}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{1}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{1}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes iY_{5}\otimes I_{6}\otimes Z_{8}\) |
\(|H_{2}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{2}\rangle _{79}|K_{2}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{2}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{2}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(iY_{3}\otimes I_{5}\otimes I_{6}\otimes Z_{8}\) |
\(|H_{3}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{3}\rangle _{79}|K_{2}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{3}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{3}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes X_{5}\otimes I_{6}\otimes Z_{8}\) |
\(|H_{4}\rangle _{79}|K_{1}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes iY_{6}\otimes iY_{8}\) |
\(|H_{4}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes iY_{6}\otimes I_{8}\) |
\(|H_{4}\rangle _{79}|K_{3}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes I_{6}\otimes X_{8}\) |
\(|H_{4}\rangle _{79}|K_{4}\rangle _{24}\) | \(|1\rangle _{1}\) | \(I_{3}\otimes Z_{5}\otimes I_{6}\otimes Z_{8}\) |
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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
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