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An efficient asymmetric bidirectional quantum teleportation protocol and the analysis of its performance over noisy environments

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Abstract

This research presents a new bidirectional quantum teleportation (BQT) protocol for transmitting two single-qubit states from Alice to Bob and a three-qubit entangled state from Bob to Alice, simultaneously. The protocol utilizes shared entanglement between the parties and requires performing two Bell-state measurements and a GHZ-state measurement. The protocol’s functionality is validated by implementing the circuit in the Qiskit library. Moreover, the effects of amplitude–damping noise and bit-flip noise are evaluated and analyzed. The protocol is compared with the recent schemes and its effectiveness is shown in terms of efficiency of the transmitted information. The protocol will contribute to the advancement of bidirectional quantum teleportation protocols.

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The data that support the findings of this study are available from the authors, upon reasonable request.

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The authors received no financial support for the research, authorship, and/or publication of this article.

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Authors and Affiliations

  1. Electrical Engineering Department, Semnan University, Semnan, Iran

    Mohammad Bolokian & Ali Asghar Orouji

  2. Electrical Engineering Department, Imam Reza International University, Mashhad, Iran

    Monireh Houshmand

Authors
  1. Mohammad Bolokian
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  2. Ali Asghar Orouji
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  3. Monireh Houshmand
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Contributions

MB: Conceptualization—Writing—original draft—Quantum computing & Software. AAO: Supervision—review & editing. MH: Supervision—Advisor—review & editing.

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Correspondence to Ali Asghar Orouji.

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Appendix 1

Appendix 1

$$ \begin{gathered} \left. {\left| \Psi \right.} \right\rangle = \left. {\left| {A_{1} A_{2} } \right.} \right\rangle \otimes |\left. {a_{1} a_{2} a_{3} a_{4} a_{5} b_{2} b_{3} } \right\rangle \hfill \\ \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{1}^{ + } } \right.} \right\rangle \left. {\left| {\phi_{1}^{ + } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {00} \right.} \right\rangle + \alpha_{0} \alpha_{1}{\prime} \left. {\left| {01} \right.} \right\rangle + \alpha_{1} \alpha_{0}{\prime} \left. {\left| {10} \right.} \right\rangle + \alpha_{1} \alpha_{1}{\prime} \left. {\left| {11} \right.} \right\rangle } \right)} \right] \hfill \\ + \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{1}^{ + } } \right.} \right\rangle \left. {\left| {\phi_{1}^{ - } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {11} \right.} \right\rangle + \alpha_{0} \alpha_{1}{\prime} \left. {\left| {10} \right.} \right\rangle + \alpha_{1} \alpha_{0}{\prime} \left. {\left| {01} \right.} \right\rangle + \alpha_{1} \alpha_{1}{\prime} \left. {\left| {00} \right.} \right\rangle } \right)} \right] \hfill \\ + \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{1}^{ + } } \right.} \right\rangle \left. {\left| {\phi_{2}^{ + } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {01} \right.} \right\rangle + \alpha_{0} \alpha_{1}{\prime} \left. {\left| {00} \right.} \right\rangle + \alpha_{1} \alpha_{0}{\prime} \left. {\left| {11} \right.} \right\rangle + \alpha_{1} \alpha_{1}{\prime} \left. {\left| {10} \right.} \right\rangle } \right)} \right] \hfill \\ + \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{1}^{ + } } \right.} \right\rangle \left. {\left| {\phi_{2}^{ - } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {10} \right.} \right\rangle + \alpha_{0} \alpha_{1}{\prime} \left. {\left| {11} \right.} \right\rangle + \alpha_{1} \alpha_{0}{\prime} \left. {\left| {00} \right.} \right\rangle + \alpha_{1} \alpha_{1}{\prime} \left. {\left| {01} \right.} \right\rangle } \right)} \right] \hfill \\ + \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{1}^{ - } } \right.} \right\rangle \left. {\left| {\phi_{1}^{ + } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {00} \right.} \right\rangle - \alpha_{0} \alpha_{1}{\prime} \left. {\left| {01} \right.} \right\rangle + \alpha_{1} \alpha_{0}{\prime} \left. {\left| {10} \right.} \right\rangle - \alpha_{1} \alpha_{1}{\prime} \left. {\left| {11} \right.} \right\rangle } \right)} \right] \hfill \\ + \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{2}^{ - } } \right.} \right\rangle \left. {\left| {\phi_{2}^{ + } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {01} \right.} \right\rangle + \alpha_{0} \alpha_{1}{\prime} \left. {\left| {00} \right.} \right\rangle - \alpha_{1} \alpha_{0}{\prime} \left. {\left| {11} \right.} \right\rangle - \alpha_{1} \alpha_{1}{\prime} \left. {\left| {10} \right.} \right\rangle } \right)} \right] \hfill \\ + \frac{1}{4\sqrt 2 } \left[ {\left. {\left| {\phi_{2}^{ - } } \right.} \right\rangle \left. {\left| {\phi_{2}^{ - } } \right.} \right\rangle \otimes \left( {\beta_{0} \left. {\left| {000} \right.} \right\rangle + \beta_{1} \left. {\left| {111} \right.} \right\rangle } \right) \otimes \left( {\alpha_{0} \alpha_{0}{\prime} \left. {\left| {10} \right.} \right\rangle + \alpha_{0} \alpha_{1}{\prime} \left. {\left| {11} \right.} \right\rangle - \alpha_{1} \alpha_{0}{\prime} \left. {\left| {00} \right.} \right\rangle - \alpha_{1} \alpha_{1}{\prime} \left. {\left| {01} \right.} \right\rangle } \right)} \right]. \hfill \\ \end{gathered} $$
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Bolokian, M., Orouji, A.A. & Houshmand, M. An efficient asymmetric bidirectional quantum teleportation protocol and the analysis of its performance over noisy environments. Opt Quant Electron 56, 1082 (2024). https://doi.org/10.1007/s11082-024-06968-6

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