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International Journal of Quantum Information

SCHEMES FOR REMOTELY PREPARING AN ARBITRARY FIVE-QUBIT BROWN-TYPE STATE

Song-Ya Ma, PING TANG, Ming‐Xing Luo

Published Jun 1, 2013• 9 citations
Publisher

Abstract

Two novel schemes via different entanglement resources are put forward to remotely preparing a five-qubit Brown-type state with high probabilities. To design the schemes, some useful measurement bases with the aid of Hurwitz matrix equation are constructed, which have no restrictions on the coefficients of the prepared state. Through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the remote preparation can be realized with the probability 50% and 100% in general case, respectively. To improve the probability, the special ensembles of the prepared state that the success probability reaches up to 100% are discussed for the first scheme by the permutation group. Furthermore, the present schemes are extended to the nonmaximally entangled quantum channel.

DOI
10.1142/s0219749913500421

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Two novel schemes via different entanglement resources are put forward to remotely preparing a five-qubit Brown-type state with high probabilities. To design the schemes, some useful measurement bases with the aid of Hurwitz matrix equation are constructed, which have no restrictions on the coefficients of the prepared state. Through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the remote preparation can be realized with the probability 50% and 100% in general case, respectively. To improve the probability, the special ensembles of the prepared state that the success probability reaches up to 100% are discussed for the first scheme by the permutation group. Furthermore, the present schemes are extended to the nonmaximally entangled quantum channel.
The application of χ state are investigated in remote state preparation (RSP). By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability 100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.
In this paper, we propose a novel scheme for deterministic joint remote state preparation (JRSP) of an arbitrary five-qubit Brown state with the assistance of several GHZ entangled states and a two-qubit unitary operation. A useful solution of joint remote preparation of an arbitrary three-qubit state is put forward firstly. Next, all senders perform appropriate projective measurement under suitable measurement basis. Finally, based on their measurement results, the target five-qubit Brown state can be prepared by introducing two auxiliary particles and making appropriate local unitary operations with success probability 1.
We present two schemes for joint remote preparation of an arbitrary four-qubit j\c{hi}i -type entangled state via three three- and (N+1)-qubit GHZ states as the quantum channel, respectively. In these schemes, two senders (or N senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, several novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations and suitable C-NOT gates. Compared with the previous schemes for the JRSP of four-qubit |\c{hi}>-type state, the advantages of the present schemes are that the total successful probability of JRSP can reach 1 and the entanglement resource can be reduced
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.
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 firstly present a novel scheme for deterministic joint remote state preparation of an arbitrary five-qubit Brown state using four Greenberg—Horme—Zeilinger (GHZ) entangled states as the quantum channel. The success probability of this scheme is up to 1, which is superior to the existing ones. Moreover, the scheme is extended to the generalized case where three-qubit and four-qubit non-maximally entangled states are taken as the quantum channel. We simultaneously employ two common methods to reconstruct the desired state. By comparing these two methods, we draw a conclusion that the first is superior to the second-optimal positive operator-valued measure only taking into account the number of auxiliary particles and the success probability.