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Chinese Physics B

Controlled remote preparation of an arbitrary four-qubit cluster-type state

Weilin Chen, Song-Ya Ma, Zhiguo Qu

Published Sep 23, 2016• 15 citations
Publisher

Abstract

Two schemes are proposed to realize the controlled remote preparation of an arbitrary four-qubit cluster-type state via a partially entangled channel. We construct ingenious measurement bases at the sender’s and the controller’s locations, which play a decisive role in the proposed schemes. The success probabilities can reach 50% and 100%, respectively. Compared with the previous proposals, the success probabilities are independent of the coefficients of the entangled channel.

DOI
10.1088/1674-1056/25/10/100304

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Two schemes are proposed to realize the controlled remote preparation of an arbitrary four-qubit cluster-type state via a partially entangled channel. We construct ingenious measurement bases at the sender’s and the controller’s locations, which play a decisive role in the proposed schemes. The success probabilities can reach 50% and 100%, respectively. Compared with the previous proposals, the success probabilities are independent of the coefficients of the entangled channel.
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.
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 several schemes for the joint remote preparation of four-qubit cluster-type states with real coefficients and complex coefficients by using six Einstein–Podolsky–Rosen (EPR) pairs and two six-qubit entangled states as quantum channels respectively. In these schemes, two senders share the original state which they wish to help the receiver to remotely prepare. It is shown that, only if two senders collaborate with each other, and perform four-qubit projective measurements on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations.
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.
Two schemes of remote preparation of a real or complex coefficients four-particle cluster-type state using two three-particle GHZ state as the quantum channel are proposed. For the entangled four-particle cluster-type state with real coefficients,a deterministic remote preparation scheme is put forward. In this scheme,two three-particle GHZ state are used as the quantum channel. Then a two-particle projective measurement should be performed by Alice,after Alice tell her measurement result to Bob,Bob can prepare the target state by performing an appropriate unitary operation with probability 1. For the more general four-particle cluster-type state with complex coefficients,another scheme is proposed,witch can successfully prepare the target state with probability 25%. And the probability of success can reach up to 50% or even 1 in some special cases. The classical communication costs in different case are discussed too.