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A general method for selecting quantum channel for bidirectional controlled state teleportation and other schemes of controlled quantum communication

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Abstract

Recently, a large number of protocols for bidirectional controlled state teleportation (BCST) have been proposed using n-qubit entangled states (\(n\in \{5,6,7\}\)) as quantum channel. Here, we propose a general method of selecting multiqubit \((n>4)\) quantum channels suitable for BCST and show that all the channels used in the existing protocols of BCST can be obtained using the proposed method. Further, it is shown that the quantum channels used in the existing protocols of BCST form only a negligibly small subset of the set of all the quantum channels that can be constructed using the proposed method to implement BCST. It is also noted that all these quantum channels are also suitable for controlled bidirectional remote state preparation. Following the same logic, methods for selecting quantum channels for other controlled quantum communication tasks, such as controlled bidirectional joint remote state preparation and controlled quantum dialogue, are also provided.

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Notes

  1. If we choose all the elements from the \(i{\hbox {th}}\) row (\(j{\hbox {th}}\) column) of S, then the desired quantum channel of the form (3) will become separable, and Charlie will lose control in one direction of the BST. Thus, the scheme will not remain BCST.

  2. This condition ensures the required bijective mapping between Charlie’s measurement outcome and the entangled states shared by Alice and Bob. In the absence of this unique mapping, the receivers will not be able to decide which unitary operation is to be applied to achieve teleportation.

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Acknowledgments

AP and KT thank Department of Science and Technology (DST), India, for support provided through the DST project No. SR/S2/LOP-0012/2010.

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Authors and Affiliations

  1. Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP, 201307, India

    Kishore Thapliyal & Anirban Pathak

  2. Jaypee Institute of Information Technology, Sector-128, Noida, UP, 201304, India

    Amit Verma

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  1. Kishore Thapliyal
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  2. Amit Verma
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Correspondence to Anirban Pathak.

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Thapliyal, K., Verma, A. & Pathak, A. A general method for selecting quantum channel for bidirectional controlled state teleportation and other schemes of controlled quantum communication. Quantum Inf Process 14, 4601–4614 (2015). https://doi.org/10.1007/s11128-015-1124-8

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