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Communications in Theoretical Physics

Probabilistic Remote Preparation of a Three-Particle Entangled State via Two Different Non-maximally Entangled Channels

You-Bang Zhan, Wang Yu-wu

Published Sep 1, 2007• 9 citations
Publisher

Abstract

We present two schemes for preparing remotely a three-particle entangled state by two different quantum channels. In the first scheme, two partial three-particle entangled states are used as the quantum channels, while in the second scheme, three two-particle non-maximally entangled states are employed as the quantum channels. It is shown that the remote state preparation can be successfully realized with certain probability, for both two schemes, if a sender performs some projective measurements and a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.

DOI
10.1088/0253-6102/48/3/013

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We present a scheme for probabilistic remote preparation of the four-particle entangled W state by using four partial entangled two-particle states as the quantum channel. In this scheme, if Alice (sender) performs four-particle projective measurements and Bob (receiver) adopts some appropriate unitary operation, the remote state preparation can be successfully realized with certain probability. The classical communication cost is also calculated. However, the success probability of preparation can be increased to 1 for four kinds of special states.
This paper presents a scheme for probabilistic remote preparation of a three-particle entangled Greenberger- Horne-Zeilinger (GHZ) state via three-particle orthonormal basis projective measurement, and then directly generalize the scheme to multi-particle case. It is shown that by using N pairs of bipartite non-maximally entangled states as the quantum channel and N -particle orthonormal basis projective measurement, the multi-particle remote preparation can be successfully realized with a certain probability.
By means of the method of the positive operator-valued measure, two schemes to remotely prepare an arbitrary two-particle entangled state were presented. The first scheme uses a one-dimensional four-particle non-maximally entangled cluster state while the second one uses two partially entangled two-particle states as the quantum channel. For both schemes, if Alice performs two-particle projective measurements and Bob adopts positive operator-valued measure, the remote state preparation can be successfully realized with certain probability. The success probability of the remote state preparation and classical communication cost are calculated. It is shown that Bob can obtain the unknown state with probability 1/4 for maximally entangled state. However, for four kinds of special states, the success probability of preparation can be enhanced to unity.