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Communications in Theoretical Physics

Canonical Quantum Teleportation of Two-Particle Arbitrary State

Xiang Hao, Shiqun Zhu

Published Aug 1, 2005• 0 citations
Publisher

Abstract

The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.

DOI
10.1088/6102/44/2/353

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The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.
Canonically conjugated observables such as position and momentum and phase and number are found to play a threefold role in quantum teleportation. First, the common eigenstate of two commuting canonical observables like phase difference and number sum provides the quantum channel between two systems. Second, a similar pair of canonical observables from another two systems is measured in the Bell-operator measurements. Finally, two translations generated by the canonically conjugated observables of a single system constitute the local unitary operation to recover the unknown state. In addition, the necessary and sufficient condition is presented for a reliable quantum teleportation of finite-level systems.
Two different teleportation protocols are investigated by using two pairs of canonically conjugated observables such as position-momentum and phase-number. The discrete variable and continuous variable quantum teleportation are unified in the framework of canonical quantum teleportation. Canonically conjugated observables are found to play a 3-fold role in the quantum teleportation. Firstly, the common eigenstate of two commuting canonical observables like phase-difference and number-sum provides the quantum channel between two systems. Secondly, a similar pair of canonical observables from another two systems is measured in the Bell operator measurements. Finally, two translations generated by the canonically conjugated observables of a single system constitute the local unitary operation to recover the unknown state.
We propose two schemes for teleporting an arbitrary three-particle state. In the first scheme, a two-particle state and a three-particle entangled state (both non-maximally entangled states) are used as quantum channels, while in the second scheme, three non-maximally entangled particle pairs are employed as quantum channels. We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations. Their success probabilities and the classical communication costs are different.
A scheme for teleporting an arbitrary three-particle W state from a sender to either of the two receivers is proposed,where the three three-particle W states quantum channel are taken as quantum channels.There are two ways to realize the intention of teleportation.It is proved that,for such maximally entangled quantum channels,there is still a certain probability of successful teleportation if the sender performs three generalized Bell-state measurements while either of the two receivers performs an appropriate unitary transformation with the help of the other suitable measurements in the basis of {|0,|1} and classical information;on the other hand,the probability of successful teleportation is not affected by the order of operations.The present scheme may be directly generalized to teleport an unknown N-particle W state from a sender to either of the two receivers by using N W states as quantum channels,as well as performing N Bell measurements.
We propose two schemes for teleporting an arbitrary three-particle state.In the first scheme,a two-particle state and a three-particle entangled state (both non-maximally entangled states)are used as quantum channels,while in the second scheme,three non-mnaximally entangled particle pairs are employed as quantum channels.We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations.Their success probabilities and the classical communication costs are different.