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Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state

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Abstract

A scheme is presented to implement bidirectional controlled quantum teleportation (QT) by using a five-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary single qubit state called qubit A to Bob and at the same time, Bob may also transmit an arbitrary single qubit state called qubit B to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional controlled QT protocol works. By using this bidirectional controlled teleportation, espcially, a bidirectional controlled quantum secure direct communication (QSDC) protocol, i.e., the so-called controlled quantum dialogue, is further investigated. Under the situation of insuring the security of the quantum channel, Alice (Bob) encodes a secret message directly on a sequence of qubit states and transmits them to Bob (Alice) supervised by Charlie. Especially, the qubits carrying the secret message do not need to be transmitted in quantum channel. At last, we show this QSDC scheme may be determinate and secure.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 61265001), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20122BAB202005 and No. 2010GZW0026 and No. 20132BAB202008), the Research Foundation of state key laboratory of advanced optical communication systems and networks, Shanghai Jiao Tong University, China (2011GZKF031104), and the Research Foundation of the Education Department of Jiangxi Province (No. GJJ13236 and No. GJJ10404 and No. GJJ13235).

Author information

Authors and Affiliations

  1. Department of physics, Jiangxi Normal University, Nanchang, 330022, China

    Yuan-hua Li, Xiao-lan Li, Ming-huang Sang, Yi-you Nie & Zi-sheng Wang

  2. Key Laboratory of Optoelectronic and Telecommunication of Jiangxi Province, Nanchang, 330022, China

    Yuan-hua Li & Yi-you Nie

  3. State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yi-you Nie

Authors
  1. Yuan-hua Li
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  2. Xiao-lan Li
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  3. Ming-huang Sang
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  4. Yi-you Nie
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  5. Zi-sheng Wang
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Corresponding author

Correspondence to Yuan-hua Li.

Appendix

Appendix

Alice’s possible measurement result, Bob’s possible measurement result, Charlie’s possible measurement result, final state with the corresponding transformation performed by Alice and Bob on qubits 4 and 3, respectively, where \(\sigma ^{i},i\in \left\{ {x,y,z} \right\} \) are Pauli matrices.

Alice’s result

Bob’s result

Charlie’s result

Final state with the receiver

Unitary transformation corresponding to the measurement outcomes (++, \(+-, -+, -\))

\(\left| {\Phi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Phi ^{\pm }} \right\rangle _{B2}\)

\(\left| 0 \right\rangle _5 \)

\(\left( {b_0 \left| 1 \right\rangle \pm b_1 \left| 0 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 0 \right\rangle \pm a_1 \left| 1 \right\rangle } \right) _3 \)

\(\sigma _4^x \otimes I_3, \sigma _4^x \otimes \sigma _3^z, -i\sigma _4^y \otimes I_3, -i\sigma _4^y \otimes \sigma _3^z \)

\(\left| {\Phi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Psi ^{\pm }} \right\rangle _{B2} \)

\(\left| 0 \right\rangle _5 \)

\(\left( {b_0 \left| 0 \right\rangle \pm b_1 \left| 1 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 0 \right\rangle \pm a_1 \left| 1 \right\rangle } \right) _3 \)

\(I_4 \otimes I_3, I_4 \otimes \sigma _3^z, \sigma _4^z \otimes I_3, \sigma _4^z \otimes \sigma _3^z \)

\(\left| {\Psi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Phi ^{\pm }} \right\rangle _{B2} \)

\(\left| 0 \right\rangle _5 \)

\(\left( {b_0 \left| 1 \right\rangle \pm b_1 \left| 0 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 1 \right\rangle \pm a_1 \left| 0 \right\rangle } \right) _3 \)

\(\sigma _4^x \otimes \sigma _3^x, \sigma _4^x \otimes -i\sigma _3^y, -i\sigma _4^y \otimes \sigma _3^x, -i\sigma _4^y \otimes -i\sigma _3^y \)

\(\left| {\Psi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Psi ^{\pm }} \right\rangle _{B2} \)

\(\left| 0 \right\rangle _5 \)

\(\left( {b_0 \left| 0 \right\rangle \pm b_1 \left| 1 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 1 \right\rangle \pm a_1 \left| 0 \right\rangle } \right) _3 \)

\(I_4 \otimes \sigma _3^x, I_4 \otimes -i\sigma _3^y, \sigma _4^z \otimes \sigma _3^x, \sigma _4^z \otimes -i\sigma _3^y \)

\(\left| {\Phi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Phi ^{\pm }} \right\rangle _{B2} \)

\(\left| 1 \right\rangle _5 \)

\(\left( {b_0 \left| 0 \right\rangle \mp b_1 \left| 1 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 1 \right\rangle \pm a_1 \left| 0 \right\rangle } \right) _3 \)

\(\sigma _4^z \otimes \sigma _3^x, \sigma _4^z \otimes -i\sigma _3^y, I_4 \otimes \sigma _3^x, I_4 \otimes -i\sigma _3^y \)

\(\left| {\Phi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Psi ^{\pm }} \right\rangle _{B2} \)

\(\left| 1 \right\rangle _5 \)

\(-\left( {b_0 \left| 1 \right\rangle \mp b_1 \left| 0 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 1 \right\rangle \pm a_1 \left| 0 \right\rangle } \right) _3 \)

\(\sigma _4^z \sigma _4^x \otimes \sigma _3^x, \sigma _4^z \sigma _4^x \otimes -i\sigma _3^y, -i\sigma _4^y \sigma _4^z \otimes \sigma _3^x, -i\sigma _4^y \sigma _4^z \otimes -i\sigma _3^y \)

\(\left| {\Psi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Phi ^{\pm }} \right\rangle _{B2} \)

\(\left| 1 \right\rangle _5 \)

\(\left( {b_0 \left| 0 \right\rangle \mp b_1 \left| 1 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 0 \right\rangle \pm a_1 \left| 1 \right\rangle } \right) _3 \)

\(\sigma _4^z \otimes I_3, \sigma _4^z \otimes \sigma _3^z, I_4 \otimes I_3, I_4 \otimes \sigma _3^z \)

\(\left| {\Psi ^{\pm }} \right\rangle _{A1} \)

\(\left| {\Psi ^{\pm }} \right\rangle _{B2} \)

\(\left| 1 \right\rangle _5 \)

\(-\left( {b_0 \left| 1 \right\rangle \mp b_1 \left| 0 \right\rangle } \right) _4 \otimes \left( {a_0 \left| 0 \right\rangle \pm a_1 \left| 1 \right\rangle } \right) _3 \)

\(\sigma _4^z \sigma _4^x \otimes I_3, \sigma _4^z \sigma _4^x \otimes \sigma _3^z, -i\sigma _4^y \sigma _4^z \otimes I_3, -i\sigma _4^y \sigma _4^z \otimes \sigma _3^z \)

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Li, Yh., Li, Xl., Sang, Mh. et al. Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inf Process 12, 3835–3844 (2013). https://doi.org/10.1007/s11128-013-0638-1

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