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Chinese Journal of Quantum Electronics

Remote preparation of arbitrary two-qubit state

Guo-Fang Shi

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Inspired by the idea of Wang and Yan's,i.e.,a two-step exact remote state preparation(RSP) of an arbitrary qubit,the remote preparation of arbitrary two-qubit state was studied.In the scheme,two non-maximally entangled GHZ states act as quantum channels.The sender Alice divides the full information encoded in known state into two parts,one purely real coefficient and the other purely real phase factor. After twice projective measurements and the transmission of 4-bit classical information by Alice,the remote receiver Bob can obtain the desired state with the success probability 4|βγ|~2 which is higher than that in Liu's protocol and it is also the advantage of our scheme,because only two-qubit state in real.Hilbert space or equatorial-like state can reach this success probability value in Liu's protocol.

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Inspired by the idea of Wang and Yan's,i.e.,a two-step exact remote state preparation(RSP) of an arbitrary qubit,the remote preparation of arbitrary two-qubit state was studied.In the scheme,two non-maximally entangled GHZ states act as quantum channels.The sender Alice divides the full information encoded in known state into two parts,one purely real coefficient and the other purely real phase factor. After twice projective measurements and the transmission of 4-bit classical information by Alice,the remote receiver Bob can obtain the desired state with the success probability 4|βγ|~2 which is higher than that in Liu's protocol and it is also the advantage of our scheme,because only two-qubit state in real.Hilbert space or equatorial-like state can reach this success probability value in Liu's protocol.
We propose a novel scheme to realize remote preparation of an arbitrary tripartite four-particle entangled state via two three-particle GHZ states as the quantum channel. In this scheme, the sender should employ several novel two-particle projective measurements on her particles. According to the sender’s measurement outcome, the receiver will carry out local unitary operations and suitable C-NOT gates on his particles to recover the desired state. It is shown that, in our scheme, the total successful probability of the RSP can reach 1.
A remote state preparation(RSP) scheme of a three-qubit Greenberger Horne Zeilinger(GHZ) class state was proposed by using three two-qubit maximally entangled states as the quantum channel.The success probability of preparation and classical communication cost were calculated.Generally speaking,according to Alice's classical message,with probability 1/4 Bob could successfully prepare the GHZ state.However,for three kinds of special states,the success probability of preparation could be increased to 1.0 after consuming some extra bits.Then the scheme was deterministic.
\n Recently Liu et al. (EPL, 87 (2009) 30006) have proposed two new schemes for probabilistically preparing arbitrary two- and three-qubit states with complex coefficients based on two- and three-qubit projective measurement, respectively. In this letter, we present a possible improvement of the successful probability for their schemes. For this purpose, we put forward two novel schemes for remote preparation of arbitrary two- and three-qubit states with complex coefficients via two and three GHZ states as the quantum channel, respectively. To complete the schemes, two novel unitary operations have been introduced. Compared with the previous schemes, the advantage of our schemes is that the total successful probability can reach 100%.\n
Abstract We present two schemes for the joint remote state preparation (JRSP) of an arbitrary tripartite four-qubit entangled state with complex coefficients via four and two three-qubit GHZ states as the quantum channel, respectively. In these schemes, the two senders share the original state which they wish to help the receiver remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if the two senders collaborate with each other, and perform projective measurements under a suitable measuring basis on their own qubits respectively, can the receiver reconstruct the original state by means of some appropriate unitary operations. We demonstrate, in our both schemes, the total success probability of the JRSP can reach 1. Moreover, compared with the first scheme in this paper, the advantage of the second scheme is that the entanglement resource can be reduced.
Recently, a scheme for deterministic remote preparation of arbitrary multi-qubit equatorial states was proposed by Wei et al. [Quantum Inf. Process. 17 70 (2018)]. It is worth mentioning that the construction of mutual orthogonal measurement basis plays a key role in quantum remote state preparation. In this paper, a simple and feasible remote preparation of arbitrary n-qubit equatorial states scheme is proposed. In our scheme, the success probability will reach unit. Moreover, there are no coefficient constraint and auxiliary qubits in this scheme. It means that the success probabilities are independent of the coefficients of the entangled channel. The advantage of our scheme is that the mutual orthogonal measurement basis is devised. To accomplish the quantum remote state preparation (RSP) schemes, some new sets of mutually orthogonal measurement basis are introduced.
In this paper, two efficient proposals are presented by using maximal slice states and orthogonal measurement basis to realize the joint remote state preparation (RSP) of two-qubit and three-qubit states, respectively. Furthermore, this kind of joint RSP schemes could be generalized to the case of arbitrary multi-qubit states, which can be transmitted from two senders to one receiver with the supervision of one manager. The successful probability of this joint RSP scheme is always equal to 100% in spite of that quantum channel is composed of non-maximally entangled states.