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International Journal of Quantum Information

SYMMETRIC AND PROBABILISTIC MULTIPARTY REMOTE STATE PREPARATION VIA THE POSITIVE-OPERATOR-VALUED MEASURE

Yimin Liu, Zhang-Yin Wang, Xiansong Liu, Zhanjun Zhang

Published Aug 1, 2009• 12 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749909005651

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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.
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.
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 multiparty-controlled remote preparation of an arbitrary m-qudit (d-dimensional quantum system) state via positive operator-valued measurement (POVM) by using nonmaximally entangled states as the quantum channel, not resorting to auxiliary qubits. The sender performs an optimal POVM measurement on her m particles with measurement operators that depend on the original state, the controllers perform generalized X-basis measurement Xdand the receiver can prepare the original state if he cooperates with all the controllers and the sender. The scheme has the advantage of having high success probability for remote preparing an arbitrary m-qudit state and more convenient than others in a practical application. Moreover, it discusses the relationship between the probability that the receiver obtains the originally state and the coefficients of the entangled states.
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.
A scheme for remotely preparing an arbitrary two-particle pure state is proposed by employing bipartite nonmaximally entangled states as quantum channels. During the preparation, two auxiliary particles and an optimal positive operator-valued measurement are introduced. The preparation of two-particle pure states can be remotely realized with certain success probability (SP). And the SP of our scheme is exactly worked out. It turns out that the SP depends inherently on the quantum channels employed beforehand. Furthermore, we find that, as far as two special ensembles of two-particle states are concerned, i.e. real and equatorial-like, the SP can be enhanced to quadruple.
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.