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International Journal of Modern Physics B

REMOTE INFORMATION CONCENTRATION VIA FOUR-PARTICLE CLUSTER STATE AND BY POSITIVE OPERATOR-VALUE MEASUREMENT

Peng Jia-yin, MING-XING LUO, Zhiwen Mo

Published Jun 20, 2013• 13 citations
Publisher

Abstract

By using a proper positive operator-valued measure (POVM), we present two new schemes for remote information concentration via four-particle cluster state. It is demonstrated that by employing a maximally entangled (respectively, nonmaximally entangled) four-particle cluster state as the quantum channel, quantum information initially and generally (respectively, specially) distributed in three spatially separated qubits can be remotely and probabilistically concentrated back to a single qubit without performing any global operations. Moreover, the total success probabilities of these two protocols are also worked out. It is more easier to realize experimentally by POVM than by projective measurement.

DOI
10.1142/s0217979213500914

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By using a proper positive operator-valued measure (POVM), we present two new schemes for remote information concentration via four-particle cluster state. It is demonstrated that by employing a maximally entangled (respectively, nonmaximally entangled) four-particle cluster state as the quantum channel, quantum information initially and generally (respectively, specially) distributed in three spatially separated qubits can be remotely and probabilistically concentrated back to a single qubit without performing any global operations. Moreover, the total success probabilities of these two protocols are also worked out. It is more easier to realize experimentally by POVM than by projective measurement.
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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.
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.
Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements, and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement (POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.
We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a four-qubit cluster-class state and a Bell-class state as the quantum channels. In the scheme, the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs. With their measurement results, the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement. Moreover, the total success probability and classical communication cost of the present protocol are also worked out.
In this paper, by using a proper positive operator-valued measurement, we propose a new tripartite scheme for probabilistically implementing quantum state sharing of an arbitrary unknown three-qubit state with two non-maximally entangled states, one is four-qubit state, another is three-qubit state. In the scheme, the Boss Alice partitions her unknown original state with two Bell-state measurements and a single-qubit projective measurement. Then she publishes her measurement results via a classical channel. With an agent Charlie's help, another agent Bob can recover the original state in probabilistic manner by performing a proper POVM.