SYMMETRIC BIDIRECTIONAL QUANTUM TELEPORTATION VIA FIVE-QUBIT CLUSTER STATE

We propose a protocol of symmetric bidirectional quantum teleportation via five-qubit cluster state. Based on the Bell-state measurements, introduces an auxiliary particle and perform joint unitary transformation, Alice wants to transmit an arbitrary two-qubit entangled state to Bob and Bob wants to transmit an arbitrary twoqubit state to Alice.


Introduction
Bidirectional quantum teleportation is a new subject in the research of quantum information.
In this paper, we propose a scheme of symmetric bidirectional quantum teleportation via fivequbit cluster state. Suppose that Alice has two particles A and B in an unknown state, she wants to transmit the state of particles A and B to Bob; at the same time, Bob has two particles C and D in an unknown state, he wants to transmit the state of particles C and D to Alice.

Symmetric Bidirectional Quantum Teleportation
Our scheme can be described as follows. Suppose Alice has qubits A and B in an arbitrary entangled state,which is described by where |a 0 | 2 + |a 1 | 2 = 1, and Bob has qubits C and D in the following state, where |b 0 | 2 + |b 1 | 2 = 1. Now Alice wants transmit the state of qubits A and B to Bob and Bob wants to transmit the qubits C and D to Alice. Assume that Alice and Bob share a five-qubit cluster state, which has the form the qubits A, B, 1 and 5 belong to Alice and qubits C, D, 2, 3 and 4 belong to Bob, respectively.
Alice firstly perform a Bell-state measurement on qubit pairs (A, 1) and Bob perform a Bellstate measurement on qubit pairs (C, 4), respectively. Then they announce their results to each other via classical channel.
In order to simplify our descriptions, without loss of generality, we take the outcome |Φ + A1 , |Φ + C4 as an example to show the principle of this symmetric bidirectional quantum teleportation protocol, where the residual qubits system collapses into the states, Alice takes X-basis measurement on qubit B and conveys her result to Bob, where X-basis is orthogonal basis including vectors, If Alice's measurement result is |+ B , then the state of the remaining qubits D, 2, 3 and 5 collapse into the state as On the other hand, Bob takes X-basis measurement on qubit D and conveys his result to Alice. If Bob's measurement result is |+ D , then the state of the remaining qubits 2, 3 and 5 collapse into the state as Also, Alice introduces an auxiliary particle 6 with an initial state|0 6 , then the state |ϕ 2 235 becomes the following state, Having performed the joint unitary transformation, the state |ϕ 3 2356 becomes the following state, After doing those operations, the symmetric bidirectional quantum teleportation is successfully realized. And other cases are given in Table 1 and 2, where Unitary transformation is given in Table 3.
So the total successful probability is equal to one.

Conclusion and discussion
In conclusion, we have proposed a theoretical scheme for symmetric bidirectional quantum teleportation. In our scheme, five-qubit cluster state is considered as the quantum channel, while Alice and Bob are not noly senders but also receivers. In this paper, Alice has two particles A and B in an unknown state, she wants to transmit the state of particles A and B to Bob; at the same time, Bob has two particles C and D in an unknown state, he wants to transmit the state of particles C and D to Alice. We hope that such a quantum teleportation scheme can be realized experimentally in the future.