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International Journal of Quantum Information

One-party controlled minimum remote state preparation of equatorial n-qubit states

Yahong Wang, Hongwei Liang

Published Sep 1, 2014• 5 citations
Publisher

Abstract

This paper offers a theoretical protocol for one-party controlled remote state preparation (RSP) of n-qubit states with minimum resources consumption. We are mainly focused on the case of the n-qubit state chosen from equatorial circle on a Bloch sphere. We use n - 1 EPR pairs and one GHZ state as quantum channel and show that only n + 1 cbits, n ebits and 2n + 1 qubits are consumed during the controlled RSP processing.

DOI
10.1142/s0219749914500385

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This paper offers a theoretical protocol for one-party controlled remote state preparation (RSP) of n-qubit states with minimum resources consumption. We are mainly focused on the case of the n-qubit state chosen from equatorial circle on a Bloch sphere. We use n - 1 EPR pairs and one GHZ state as quantum channel and show that only n + 1 cbits, n ebits and 2n + 1 qubits are consumed during the controlled RSP processing.
In this paper, we propose three schemes for remotely state preparation (RSP) an arbitrary two-level one-atom state via cavity quantum electro dynamics (QED) with minimal resources consumption. In the first case, a Greenberger–Horne–Zeilinger (GHZ) state is used as quantum channel; in the second case, the sender needs to construct an quantum channel with both of the assistant of cavity QED and the knowledge about the state to be remotely prepared. In each scheme, only 1 cbit and 1 ebit are needed with the aid of cavity QED. In the third case, we combine the first two protocols and give a theoretical proposal for controlled RSP with only 2 cbits and 1 ebit resources consumption.
Remote state preparation (RSP) is a technique to transmit quantum states with classical communication and previously shared entanglement. In this paper, we consider RSP in a multiparty setting. A simple yet nontrivial case is studied, where there is one sender and two receivers. We put forth a broadcasting method for developing multiparty RSP protocols. We show that this method can remotely prepare arbitrary states by consuming classical and quantum resources. For preparing highly entangled states, the proposed method achieves the lower bound for the amount of consumed resources asymptotically.
We have experimentally implemented remote state preparation (RSP) of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform 13^{13}13CHCl3_{3}3​ over interatomic distances using liquid-state nuclear magnetic resonance (NMR) technique. Full RSP of a special ensemble of qubits, i.e., a qubit chosen from equatorial and polar great circles on a Bloch sphere with Pati's scheme, was achieved with one cbit communication. Such a RSP scheme can be generalized to prepare a large number of qubit states and may be used in other quantum information processing and quantum computing.
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.
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.