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Chinese Physics

A new representation and probabilistic teleportation of an arbitrary and unknown N -particle state

Li Dong, Xiu Xiao-Ming, Gao Ya-Jun

Published Nov 2, 2006• 18 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/15/12/011

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Chinese Journal of Quantum Electronics•Jan 1, 2006•0 citations
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.
Two schemes for teleporting an unknown one-particle state are proposed when a general W state is utilized as quantum channel. In the first scheme, after the sender (Alice) makes a Bell-state measurement on her particles, the recipient (Bob) performs a Von Neumann measurement and introduces an auxiliary particle, and carries out a unitary transformation on his particle and the auxiliary particle, and performs a Von Neumann measurement on the auxiliary particle to confirm whether the teleportation succeeds or not. In the second scheme, the recipient (Bob) does not need to perform the first Von Neumann measurement or introduce the auxiliary particle, which is necessary in the first scheme. It is shown that the maximal probabilities of successful teleportation of the two schemes are identical if the recipient (Bob) performs an appropriate unitary transformation and adopts a proper particle on which he recovers the quantum information of state to be teleported.
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.
In this paper a new scheme for teleporting an unknown entangled state of two particles is proposed. To weaken the requirement for the quantum channel, without loss of generality, two communicators only share a non-maximally entangled two-particle state. Teleportation can be probabilistically realized if sender performs Bell-state measurements and Hadamard transformation and receiver introduces two auxiliary particles, operates C -not operation, single-qubit measurements and appropriate unitary transformations. The probability of successful teleportation is determined by the smaller one among the coefficients' absolute values of the quantum channel.