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Communications in Theoretical Physics

Probabilistic Teleportation of an Arbitrary Two-Particle State and Its Quantum Circuits

Zhan-Ying Guo, Fang Jian-Xing, Zhu Shi-Qun, Xuemin Qian

Published Jun 1, 2006• 4 citations
Publisher

Abstract

Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.

DOI
10.1088/0253-6102/45/6/012

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Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.
We present a scheme to probabilistically teleport an arbitrary and unknown two-particle state via a nonmaximally entangled EPR pair and a non-maximally entangled GHZ state as the quantum channel. With the help of Bell-state measurements and Hadamard measurement, an arbitrary two-particle state can be perfectly teleported if a receiver introduces a collective unitary transformation. The unitary transformation is given uniquely. Also, we present a quantum circuit for realizing the teleportation successfully.
A new representation of an arbitrary and unknown N -particle state is presented at first. As an application, a scheme for teleporting an arbitrary and unknown N -particle state is proposed when N pairs of two-particle non-maximally entangled states are utilized as quantum channels. After Alice (sender) makes Bell-state measurement on her particles, Bob (recipient) introduces an auxiliary particle and carries out appropriate unitary transformation on his particle and the auxiliary particle depending on classical information from Alice. Then, von Neumann measurement that confirms whether the teleportation succeeds or not is performed by Bob on the auxiliary particle. In order to complete the teleportation, another N -1 times operations need to be performed which are similar to the above ones. It can be successfully realized with a certain probability which is determined by the product of the smaller coefficients of non-maximally entangled pairs. All possible unitary transformations are given in detail.
We present a scheme to probabilistically teleport an arbitrary and unknown three-particle state via a two-particle non-maximally entangled state and a four-particle non-maximally entangled state as the quantum channel. With the help of Bell-state measurements, an arbitrary three-particle state can be perfectly teleported if a receiver introduces a collective unitary transformation. All kinds of unitary transformations are given in greater detail. This scheme can be generalized to the teleportation of an arbitrary and unknown multiparticle state.
A scheme for controlled teleportation of an arbitrary two-particle state using a maximally entangled EPR pair and a cluster state as the quantum channel is proposed. After receiving Alice's Bell state measurement results, the controller performs a joint measurement on his particles under a non-maximally entangled Bell-basis. The receiver needs to introduce an auxiliary qubit, and performs a series of appropriate unitary transformations on his particles. The original state can be teleported successfully with the probability 2 cos2 θ.
A scheme for controlled teleportation of an arbitrary two-particle state using a maximally entangled EPR pair and a cluster state as the quantum channel is proposed.After receiving Alice's Bell state measurement results, the controller performs a joint measurement on his particles under a non-maximally entangled Bell-basis.The receiver needs to introduce an auxiliary qubit,and performs a series of appropriate unitary transformations on his particles.The original state can be teleported successfully with the probability 2 cos2 9.
A scheme of teleportation of an arbitrary three-particle state is presented when a non-maximal arbitrary five-particle state and an EPR pair are used as quantum channels. We show that teleportation can be successfully (realized) with a certain probability by performing three Bell-state measurements on the sender's side and by (introducing) an auxiliary particle and performing a unitary transformation the Hadamard operation and measurement result, conditioning on the other possible receiver's side.