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Quantum Information Processing

On the role of the four-qubit state in two-qubit gate teleportation

Paulo Sousa, F. V. Mendes, Rubens Viana Ramos

Published Feb 4, 2016• 0 citations
Publisher
DOI
10.1007/s11128-015-1108-8

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We introduce the concept of the Bell transform to represent known quantum gates in the literature, which are a unitary basis transformation from the product basis to the Bell states or the Greenberger-Horne-Zeilinger (GHZ) states. The algebraic structure of the four dimensional Bell transform has been studied systematically in this paper and we point out that it may be not a Clifford gate. The representative examples of the four dimensional Bell transform are verified as maximally entangling Clifford gates and some of them are recognized as parity-preserving gates or matchgates or Yang--Baxter gates. We define the teleportation operator in terms of the four dimensional Bell transform and apply it to the reformulation of the fault-tolerant construction of single-qubit gates and two-qubit gates in teleportation-based quantum computation. The algebraic structure of the higher dimensional Bell transform is also included and representative examples for it are verified as multi-qubit Clifford gates. Our research suggests that the Bell transform may play important roles in quantum information and computation as a new type of quantum transform.
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.
Abstract Based on the four-qubit cluster state as quantum channel, we put forward a novel scheme for teleporting a two-qubit arbitrary entangled state. The necessary quantum operations for accomplishing the task are two controlled-not gate operations, one controlled-phase gate operation, four single-qubit measurements and two single-qubit transformed operations. They are easily achievable with current experimental techniques. Besides, the present scheme is deterministic because its probability of success is 100 % .