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arXiv:2302.11300 · International Journal of Quantum Information

Bi-directional quantum teleportation of GHZ-like states

Leila S. Tabatabaei, Babak Vakili

Published Aug 20, 2023• 9 citations

Abstract

In this paper, we propose a method through which [Formula: see text]-qubit states can simultaneously be bi-directionally transmitted between two users. We assume that Alice and Bob, the legitimate users, each have a [Formula: see text]-qubit GHZ-like state and want to teleport it to the other party. Also, a four-qubit cluster state plays the role of the quantum channel of this bi-directional quantum teleportation. The protocol is based on the method that at first, each user, through a series of [Formula: see text] gates, converts the [Formula: see text]-qubit state into a single qubit and some [Formula: see text] qubits. Then, by means of the Bell state measurement and proper operation, the single qubit state is transferred over the channel between the two sides. By re-applying the [Formula: see text] gates on the transmitted qubits and auxiliary [Formula: see text] states, each user reconstructs the initial GHZ-like state. Finally, we investigate the effects of some kind of noises on the density matrix of the channel due to its interaction with the environment and present a method to protect the channel against the bit-flip error.

DOI: 10.1142/s0219749923500351

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In this paper, we propose a method through which [Formula: see text]-qubit states can simultaneously be bi-directionally transmitted between two users. We assume that Alice and Bob, the legitimate users, each have a [Formula: see text]-qubit GHZ-like state and want to teleport it to the other party. Also, a four-qubit cluster state plays the role of the quantum channel of this bi-directional quantum teleportation. The protocol is based on the method that at first, each user, through a series of [Formula: see text] gates, converts the [Formula: see text]-qubit state into a single qubit and some [Formula: see text] qubits. Then, by means of the Bell state measurement and proper operation, the single qubit state is transferred over the channel between the two sides. By re-applying the [Formula: see text] gates on the transmitted qubits and auxiliary [Formula: see text] states, each user reconstructs the initial GHZ-like state. Finally, we investigate the effects of some kind of noises on the density matrix of the channel due to its interaction with the environment and present a method to protect the channel against the bit-flip error.

In this paper, a theoretical scheme for bidirectional quantum teleportation by using a four-qubit GHZ state and two Bell states as a quantum channel is proposed. In this scheme, two arbitrary single-qubit quantum states and an unknown three-qubit state can be mutually transmitted between the two communication participants Alice and Bob. The quantum state information can be transmitted if Alice performs four single-qubit measurement operations on her qubits and Bob carries out a four-qubit joint measurement on his qubits, respectively. Then both Alice and Bob can reconstruct the target quantum state by means of appropriate unitary operations. Then we take comparisons with the other bidirectional quantum teleportation protocols in five aspects of quantum information bits transmitted, necessary operations, consumption of quantum resource, consumption of classical resource and intrinsic efficiency. Furthermore, we use channel authentication method to ensure the channel security and prove that our protocol can withstand four attack scenarios. It is concluded that our scheme has significant advantages of more qubits number transmitted, higher intrinsic efficiency and high security.

Recently, Li and Nie (Int. J. Theo. Phys. 52:1630, 2013) had introduced a bidirectional controlled quantum teleportation (BCQT) protocol by using GHZ-Bell state as a quantum channel. Also, Shukla et al. (Int. J. Theo. Phys. 52:3790, 2013) had shown the Li and Nie (LN) protocol is not a BCQT scheme. In this paper, two kinds of bidirectional teleportation schemes in order to correct and improve LN protocol are presented. In the first scheme, Alice and Bob as two legitimate users can simultaneously teleport an unknown single-qubit state to each other with the help of controller Charlie. In the second scheme, Alice can transmit two-qubit entangled state to Bob and at the same time Bob can teleport single-qubit state to Alice. In both of proposed schemes the quantum channel linking users is a GHZ-Bell state.

A scheme of two-way teleportation was proposed,with GHZ quadripartite entangled state as quantum channel.Two sides of communication(Alice and Bob) shared two pairs of GHZ quadripartite entangled state in advance.After communication,Alice and Bob performed quantum projection measurement on their own qubits respectively,and announced the measured results via classical channel.Then according to the measured results presented by the other party,Alice and Bob can make appropriate unitary transformations that its own party can reconstruct the opposite quantum state information,and thus the whole two-way teleportation was realized.As long as the both sides of communication chose the suitable GHZ entangled state as quantum channel and distributed the entangled partites imparity and properly in advance,two-way teleporting including unknown general one qubit and two qubits entangled Bell state or three qubits entangled GHZ state could be realized respectively.

Quantum teleportation is considered as the most basic process of quantum communication. It is undoubtedly beneficial for the realization of quantum teleportation while transmitting the maximum number of quantum bits with the minimum number of quantum channel resources. An improved bidirectional quantum teleportation protocol based on a quantum channel of six-qubit cluster state is proposed. In this paper, the user Alice can transmit an unknown three-qubit entangled state to the user Bob, and at the same time, the user Bob can transmit an arbitrary single-qubit state to the user Alice by utilizing GHz-state measurement, bell-state measurement, single-qubit Von Neumann measurement, and unitary operations. Compared with other schemes in quantum resource consumption, necessary operation complexity including operation difficulty and intensity, classical resource consumption, quantum information bits transmitted, and intrinsic efficiency, our scheme has the remarkable advantages in transmitting more quantum information and possesses higher intrinsic efficiency.

Abstract This paper proposes a symmetric bidirectional quantum teleportation protocol through an eight-qubit cluster state as a quantum channel to achieve GHZ state interchange between two parties. Alice and Bob must first perform two CNOT gate operations on the unknown GHZ state to be sent in our scheme. Next, they need to complete the Bell state measurements and the corresponding unitary operations to obtain the corresponding GHZ state. Our protocol has lower operational complexity and higher inherent efficiency compared to other protocols. In addition, we have simulated the quantum circuit on the IBM qasm simulator to verify the feasibility of the protocol.