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Journal of Hunan University of Arts and Science

Realization of deterministic remote state preparation using a partially entangled state

Chunmei Yao

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

A scheme is proposed for remotely preparing a state exactly via any pure shared entangled state with entanglement-assistance under local operations and classical communication. This scheme consists of a generalized measurement described by a positive operator-valued measure (POVM), one- way classical communication, and corresponding unitary operations. Firstly, the case of a 2-dimensional partially entangled channel is discussed, and then generalizes this scheme to higher-dimensional case.

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A scheme is proposed for remotely preparing a state exactly via any pure shared entangled state with entanglement-assistance under local operations and classical communication. This scheme consists of a generalized measurement described by a positive operator-valued measure (POVM), one- way classical communication, and corresponding unitary operations. Firstly, the case of a 2-dimensional partially entangled channel is discussed, and then generalizes this scheme to higher-dimensional case.
We present a general scheme for multiparty joint remote preparation of an arbitrary m -qudit state with a pure entangled quantum channel via positive operator-valued measurement (POVM). The n senders share the information of the prepared state. The first sender performs POVM on his particles according to his knowledge of the original state, the other n − 1 senders perform m -particle projective measurement and the receiver can probabilistically reconstruct the original state by performing unitary operations on his particles according to the senders' measurement results. The scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m -qudit state via pure entangled quantum states. Moreover, it discusses the relationship between the coefficients of the pure entangled states and the success 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.
We present a scheme for symmetric controlled remote preparation of an arbitrary 2-qudit state form a sender to either of the two receivers via positive operator-valued measurement and pure entangled two-particle states. The first sender transforms the quantum channel shared by all the agents via POVM according to her knowledge of prepared state. All the senders perform single- or two-particle projective measurements on their entangled particles and the receiver can probabilisticaly reconstruct the original state on her entangled particles via unitary transformation and auxiliary qubit. The scheme is optimal as the probability which the receiver prepares the original state equals to the entanglement of the quantum channel. Moreover, it is more convenience in application than others as it requires only two-particle entanglements for preparing an arbitrary two-qudit state.
We propose a scheme to remotely prepare a general two-particle entangled state by using a bipartite entangled state and a tripartite entangled W state as the quantum channel. Our scheme consists of one sender and two remote receivers. The sender can help either one of the receivers to remotely reconstruct the original state with the assistance of the other receiver's single-particle orthogonal measurement. We obtain the total success probability and discuss the classical communication cost in our remote state preparation scheme.
I present a novel tripartite scheme for remotely preparing an arbitrary two-qubit state with two three-qubit entanglements. By using a proper positive operator-valued measure (POVM), it is shown the remote two-qubit preparation can be realized in either distant ministrant's place in a probabilistic manner via their collaboration. I also explore its applications to six special ensembles of state in detail. The extensive investigations shows that the remote preparation can be achieved with higher probability provided that the prepared state belongs to the six special ensembles.
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.