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The Journal of Atomic and Molecular Sciences

Symmetric Remote Two-Qubit Preparation via Positive Operator-Valued Measure

Zhang-Yin Wang, Xing-Qiang Yang

Published Jan 1, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.4208/jams.061310.071210a

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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.
We present a tripartite scheme for a preparer to remotely prepare an arbitrary single-qubit state in either distant ministrant's place by using a GHZ-type state. After the preparer's single-qubit state projective measurement, by performing a proper positive operator-valued measure, one ministrant can construct the preparer's state in a probabilistic manner with the other ministrant's assistance. Furthermore, we show that the remote state preparation can be achieved with a higher probability provided that the prepared state belongs to two special ensembles. Finally, we sketch the generalization of the tripartite scheme to a multiparty case.
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.
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.
I present a new scheme for probabilistic remote preparation of a general two-qubit state from a sender to either of two receivers. The quantum channel is composed of a partial entangled tripartite Greenberger—Horne—Zeilinger (GHZ) state and a W-type state. I try to realize the remote two-qubit preparation by using the usual projective measurement and the method of positive operator-valued measure, respectively. The corresponding success probabilities of the scheme with different methods as well as the total classical communication cost required in this scheme are also calculated.
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.
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.