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The Journal of Atomic and Molecular Sciences

Implementations for Remotely Preparing Single- and Two-Particle States in a Four-Level System

Dong Wang

Published May 27, 2010• 0 citations
Publisher

Abstract

We propose two schemes to realize remote state preparation (RSP). The first scheme is designed to prepare an arbitrary single-particle state in a four-level system with the aid of one bipartite maximally entangled channel, which is then generalized to the second scheme, i.e., RSP for a two-particle state in a four-level system. During the two preparations, one single-particle projective measurement and one two-particle projective measurement are performed respectively. Our results show that the preparation for single-particle or two-particle states can be remotely realized with at least 25% successful probability and unit fidelity. Furthermore, with respect to two special ensembles of the prepared states, i.e., real and equatorial-like, the successful probability can be pushed up to 100%. Hence our probabilistic schemes become deterministic ones.

DOI
10.4208/jams.011310.042910a

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We propose two schemes to realize remote state preparation (RSP). The first scheme is designed to prepare an arbitrary single-particle state in a four-level system with the aid of one bipartite maximally entangled channel, which is then generalized to the second scheme, i.e., RSP for a two-particle state in a four-level system. During the two preparations, one single-particle projective measurement and one two-particle projective measurement are performed respectively. Our results show that the preparation for single-particle or two-particle states can be remotely realized with at least 25% successful probability and unit fidelity. Furthermore, with respect to two special ensembles of the prepared states, i.e., real and equatorial-like, the successful probability can be pushed up to 100%. Hence our probabilistic schemes become deterministic ones.
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.
Using partial entangled states as the quantum channel, two schemes for probabilistic remote preparation of the four-particle cluster-type state with real and complex coefficients are presented. In the first scheme, the sender and the receiver share two partial Bell states and one partial three-qubit GHZ stats as the quantum channel, and the sender can help a remote receiver to prepare a four-particle entangled cluster-type state by using three-qubit projective measurements with certain probability. In the second scheme, the quantum channel is composed of two partial three-qubit GHZ states, the remote state preparation (RSP) can be successfully realized via the positive operator valued measure (POVM), and the two-particle projective measurements are also needed in this process. The total success probability and classical communication cost are calculated.
In this paper, two novel schemes for deterministic joint remote state preparation (JRSP) of arbitrary single- and two-qubit states are proposed. A set of ingenious four-particle partially entangled states are constructed to serve as the quantum channels. In our schemes, two senders and one receiver are involved. Participants collaborate with each other and perform projective measurements on their own particles under an elaborate measurement basis. Based on their measurement results, the receiver can reestablish the target state by means of appropriate local unitary operations deterministically. Unit success probability can be achieved independent of the channel's entanglement degree.
We present a scheme for remotely preparing an arbitrary two-qubit pure state by using two bipartite partially entangled states as the quantum channel, the scheme is then generalized to the arbitrary three-qubit case. For the two cases of remote state preparation, we construct two different efficient projective measurement bases at sender's side and calculate the corresponding success probabilities. It is shown that remote preparation of the two-qubit or three-qubit state can be probabilistically achieved with unity fidelity. Moreover, for some special ensembles of the initial states, we find that the success probability of preparation can be increased to four times for two-qubit states and eight times for three-qubit states, and is equal to one in the case of the maximal entanglement resources.
We propose a novel scheme to realize remote preparation of an arbitrary tripartite four-particle entangled state via two three-particle GHZ states as the quantum channel. In this scheme, the sender should employ several novel two-particle projective measurements on her particles. According to the sender’s measurement outcome, the receiver will carry out local unitary operations and suitable C-NOT gates on his particles to recover the desired state. It is shown that, in our scheme, the total successful probability of the RSP can reach 1.
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.