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Modern Physics Letters B

QUANTUM KEY DISTRIBUTION AND REMOTE STATE PREPARATION VIA CLUSTER STATE

Guo-Fang Shi

Published Apr 20, 2010• 6 citations
Publisher

Abstract

In this paper, the schemes of quantum key distribution and remote state preparation of an arbitrary two-qubit state via four-particle cluster state are proposed. The efficiency of the former is 1 and the probability of the latter is 1(1/4) if the coefficients are real (complex).
DOI
10.1142/s0217984910023049

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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.
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.
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.