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Communications in Theoretical Physics

A universal protocol for bidirectional controlled teleportation with network coding

Meng-Yao He, Song-Ya Ma, Kun-Peng Kang

Published Jul 6, 2021• 15 citations
Publisher

Abstract

Abstract We investigate bidirectional teleportation that works in a fair and efficient manner. Two explicit protocols are proposed to realize bidirectional teleportation with a controller. One is a symmetric protocol for two-qubit states. The other is an asymmetric protocol for single- and two-qubit states. We then devise a universal protocol for arbitrary n 1 - and n 2 -qubit states via a (2 n 1 + 2 n 2 + 1)-qubit entangled state, where n 1 ≤ n 2 . The receiver only needs to perform the single-qubit recovery operation, which is derived by a general expression. Moreover, a (2 n 1 + 1)-bit classical communication cost can be saved within the controller’s broadcast channel by the use of network coding technology.

DOI
10.1088/1572-9494/ac1168

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In this paper, a novel protocol for bidirectional controlled quantum teleportation (BCQT) is proposed. Based on entanglement swapping of initiate Bell state, two users can teleport an unknown single-qubit state to each other under the permission of the supervisor. This proposed protocol would be utilized to a system in which a controller controls the communication in one direction only. Indeed, just one of the users needs the permission of the controller to reconstruct the unknown quantum state. In comparison to the existing BCQT protocols which their quantum channels are cluster and brown state, the proposed protocol is more practical within todays technology, since it merely uses Bell states as the quantum resource.
In this paper, different from the other existing methods that only the special and limited numbers of qubits transmit between Alice and Bob, a general method is proposed to implement Bidirectional Quantum Controlled/uncontrolled Teleportation (BQCT/BQT) that Alice and Bob can transmit each type of arbitrary n and m-qubits to each other, simultaneously. This protocol is based on Controlled-NOT (CNOT) operation, appropriate single-qubit unitary operations and single-qubit measurement in the Z-basis and X-basis. Also, the quantum channel can be created by using Hadamard and CNOT operations. One of the advantages of this method is using the single-qubit measurements which are more efficient than two-qubit measurements.
In this paper, an asymmetric bidirectional controlled quantum teleportation via a six-qubit partially entangled state is given, in which Alice wants to transmit a two-qubit entangled state to Bob and Bob wants to transmit a single-qubit state to Alice on the same time. Although the six-qubit state as quantum channel is partially entangled, the teleportation is implemented deterministically. Furthermore, only Bell-state measurements, single-qubit measurements and some unitary operations are needed in the scheme.