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Journal of Physics B Atomic Molecular and Optical Physics

Joint remote preparation of four-qubit cluster-type states revisited

Nguyen Ba An, Cao Thi Bich, Nung Van Don

Published Jun 21, 2011• 37 citations
Publisher

Abstract

We revisit the protocols proposed recently ( Zhan et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 095501 ) for joint remote preparation of four-qubit cluster-type states. We not only point out errors in those protocols but also make considerable improvements. Our protocols, for both the cases of real and complex coefficients of the state to be prepared, consume much less quantum resource as well as classical communication cost.

DOI
10.1088/0953-4075/44/13/135506

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We revisit the protocols proposed recently ( Zhan et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 095501 ) for joint remote preparation of four-qubit cluster-type states. We not only point out errors in those protocols but also make considerable improvements. Our protocols, for both the cases of real and complex coefficients of the state to be prepared, consume much less quantum resource as well as classical communication cost.
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Designing quantum protocols with unit success probability is highly desirable from a viewpoint of the overall resource cost. In this work, we propose a new deterministic protocol for joint remote preparation of the most general two-qubit state using the same quantum/classical resource as in [An et al., Phys. Lett. A {\bf 375} (2011) 3570] and, at the same time, retaining the passive role of the receiver as in [Xiao et al., J. Phys. B: At. Mol. Opt. Phys. {\bf 44} (2011) 075501], which employs a different kind of nonlocal resource. From a practical point of view, this protocol proves most suitable in situations when only Einstein- Podelsky-Rosen pairs are supplied and the receiver is not capable of performing any measurements nor controlled-NOT gates.
A scheme is proposed for remotely preparing a two-qubit state by using four-qubit cluster state as the quantum channel.In the scheme,the success probability of preparation and classical communication cost are calculated.In general,Bob can successfully prepare the target state with the probability 1/4 and consume only 1/4 bits classical communication.However,if the state belongs to six special situations,the success probability of preparation can reach 1/2 or even 1 after consuming some extra bits.
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.
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.