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Communications in Physics

Nonmaximal Entanglement Can Make Joint Remote State Preparation Absolutely Secure

Cao Thi Bich, Nguyen Ba An

Published May 21, 2013• 0 citations
Publisher

Abstract

Joint remote state preparation is a multiparty global quantum task in which several parties are assigned to jointly prepare a quantum state for a remote party. Although various protocols have been proposed so far, none of them are absolutely secure in the sense that the legitimate parties (the preparers plus the receiver) can by no means identify the state to be prepared even if they all collude with each other. Here we resolve this drawback by employing the quantum channel in terms of nonmaximally entangled states whose parameters are kept secret to all the participants but used to split the information in a judicious way so that not only absolute security in the above-mentioned sense is achieved but also the performance is the simplest possible.

DOI
10.15625/0868-3166/23/2/2857

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Joint remote state preparation is a multiparty global quantum task in which several parties are assigned to jointly prepare a quantum state for a remote party. Although various protocols have been proposed so far, none of them are absolutely secure in the sense that the legitimate parties (the preparers plus the receiver) can by no means identify the state to be prepared even if they all collude with each other. Here we resolve this drawback by employing the quantum channel in terms of nonmaximally entangled states whose parameters are kept secret to all the participants but used to split the information in a judicious way so that not only absolute security in the above-mentioned sense is achieved but also the performance is the simplest possible.
Noise is unavoidable in practice and its presence makes quantum protocols imperfect. In this paper we consider a way to cope with typical types of noise in joint remote preparation of an arbitrary 2-qubit state. The idea is to use nonmaximally (in stead of maximally) entangled states as the initial quantum channel. Because noise changes the initial quantum channel we can beforehand tailor it to be nonmaximally entangled by introducing free parameters which, depending on given types of noise, can be controlled so that due to the affect of noise the initial quantum channel becomes closest to the maximally entangled one, thus optimizing the performance of the joint remote state preparation protocol. The dependence of the optimal averaged fidelities on the strength of various types of noise is represented by phase diagrams that clearly separate the quantum domain from the classical one.
Abstract Ideal deterministic quantum communication tasks require maximally entangled channels. The reality is that the maximally entangled channel is inevitably degraded to a generally entangled one because of various decoherence mechanisms, seriously deteriorating the performance of quantum communication. In most cases, entanglement purification and distillation are utilized to improve the entanglement and to construct the maximally entangled channel. In this paper, we proposed an alternative scheme to realize deterministic joint remote state preparation using a non-maximally entangled channel. Instead of spending additional entanglement resources in advance for entanglement purification or distillation, only two non-entangled ancillaries are employed in this scheme. Whether the employed quantum channel is a maximally entangled channel or a generally entangled one, remote state preparation would never fail theoretically in this investigation. This protocol provides a feasible way for the construction of practical quantum networks.
We propose two protocols for joint, multi-party remote preparation of qudit states by using a d-level six-qudit Cluster state as the quantum channel. The first protocol is used for the joint remote preparation of an arbitrary two-qudit state via the d-level six-qudit Cluster state. The second is used for bi-directional joint remote preparation of an arbitrary single-qudit state via a d-level six-qudit Cluster state. All senders share information about the prepared state. The first sender applies Positive Operator-Valued Measurement (POVM) on her entangled particles in accordance with her information about the prepared state, while the second sender performs projective measurements in accordance with the information about the prepared state and the first sender’s measurement results. The receiver can prepare the original state by performing a corresponding unitary operation according to the measurement results from all the senders. These two protocols have the advantage of being able to provide a high channel capacity by using a d-level Cluster state as the quantum channel.
The quantum equatorial state, a special kind of quantum state, has attracted much attention because of its potential for applications in quantum information processing. The remote preparations of arbitrary two-qudit, three-qudit equatorial and m-qudit equatorial states have been studied via different entangle quantum channels. In this paper, we propose two protocols for the controlled joint remote preparation of an arbitrary m-qudit equatorial state with a pure entangled quantum channel. The first is for the controlled joint remote preparation of the m-qudit equatorial state by using m multiparticle GHZ-class states as the quantum channel, and the second is for the controlled joint remote preparation of the m-qudit equatorial state via a multiparticle entangled state. All senders share information about the prepared state and perform m-particle projective measurements on their entangled particles according to their information about the prepared state. All controllers perform generalized X-basis measurements on their entangled particles. If a receiver cooperates with all the senders and controllers, he can prepare the original state probabilistically by performing unitary operations on his entangled particles and an auxiliary qubit. This protocol is more convenient for applications because it only requires nonmaximal entanglement for the controlled joint remote preparation of an arbitrary m-qudit equatorial state.
In this paper, we propose a novel scheme for deterministic hierarchical joint remote state preparation (HJRSP). Two senders and three receivers are involved. One sender has the amplitude information of the target state to be prepared at the receiver's port, while the other one has the phase information. There is a hierarchy among the receivers concerning their powers to reconstruct the target state. 6-particle partially entangled state is used as the quantum channel. Participants perform projective measurements under elaborate measurement bases. According to their measurement results, the receiver reconstructs the target state by means of appropriate unitary operation. The higher-power receiver reconstructs the target state independently, and the lower-power receiver reconstructs the target state if and only if all the other receivers help him (her). Different from the previous HJRSP scheme utilizing partially entangled channels, auxiliary qubit is not required in our scheme, and unit success probability can be achieved. It is shown that the success probability is independent of the parameters of the partially entangled quantum channel.