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Communications in Theoretical Physics

Deterministic Remote State Preparation via the χ State*

Pei Zhang, Xian Li, Song-Ya Ma, Zhiguo Qu

Published May 1, 2017• 10 citations
Publisher

Abstract

Abstract Two deterministic schemes using the χ state as the entangled channel are put forward to realize the remote preparation of arbitrary two- and three-qubit states. To design the schemes, we construct sets of ingenious measurement bases, which have no restrictions on the coefficients of the prepared state. At variance with the existing schemes via the χ state, the success probabilities of the proposed schemes are greatly improved.

DOI
10.1088/0253-6102/67/5/498

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Abstract Two deterministic schemes using the χ state as the entangled channel are put forward to realize the remote preparation of arbitrary two- and three-qubit states. To design the schemes, we construct sets of ingenious measurement bases, which have no restrictions on the coefficients of the prepared state. At variance with the existing schemes via the χ state, the success probabilities of the proposed schemes are greatly improved.
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.
\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
In this paper, two novel schemes for deterministic joint remote state preparation (JRSP) of arbitrary single- and two-qubit states are proposed. A set of ingenious four-particle partially entangled states are constructed to serve as the quantum channels. In our schemes, two senders and one receiver are involved. Participants collaborate with each other and perform projective measurements on their own particles under an elaborate measurement basis. Based on their measurement results, the receiver can reestablish the target state by means of appropriate local unitary operations deterministically. Unit success probability can be achieved independent of the channel's entanglement degree.
This paper offers a theoretical protocol for deterministic controlled remote state preparation of arbitrary real-parameter multi-qubit states, in which the maximally three-qubit entangled states are used as quantum channel. We elaborate the processes of implementing remote state preparation of the real-parameter two- and three-qubit states, and extend the protocol to realize the real-parameter n-qubit states. By performing the appropriate multi-qubit projective measurement basis and multi-qubit unitary operations, the successful probability of our scheme can reach 100%.
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.