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Communications in Physics

Coping with noise in joint remote preparation of a general two-qubit state by using nonmaximally entangled quantum channel

Dat Thanh Le, Hop Van Nguyen, Nguyen Ba An

Published Apr 26, 2018• 20 citations
Publisher

Abstract

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.

DOI
10.15625/0868-3166/28/1/11722

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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.
We address the issue of improving the quality of the joint remote preparation of an arbitrary two-qubit in case four qubits of the quantum channel which consists of a GHZ state and a GHZ-like one are subjected to noises. Two controlling parameters are added, one in the quantum channel and other in the measurement of the second sender, in order to optimize the averaged fidelities. The results from analyzing the behaviors of the optimal averaged fidelities show that there are essentially two different ways for the optimization of the efficiency of the protocol. The first is simply choosing suitably the quantum channel as well as the measurement in which the desired fidelity can be found in large values of noisy parameters. The second is by means of interactions between qubits and dissipative environments whose result is more noises more fidelity.
A main obstacle faced by any quantum information processing protocol is the noise that degrades the desired coherence/entanglement. In this work we study by means of Kraus operators the effect of four typical types of noises on the quality of joint remote state preparation of a single-qubit state using a three-qubit Greenberger–Horne–Zeilinger-type state as the initial quantum channel. Assuming that two of the three involved qubits independently suffer a type of noise, we derive analytical expressions not only for the optimal averaged fidelities but also for the boundaries in phase space of the domains in which the joint remote state preparation protocol outperforms the classical one. Detailed discussion is given for each of the total 16 noisy scenarios. We also provide physical interpretation for the obtained results and outline possible future topics.
In this paper, we discuss a protocol for preparing a non-maximally entangled W-state at a distant location where there are two parties intending such creation each of whom possesses only partial information about the state. These two parties along with a third party Controller, participate in a single protocol in order to create the intended state in the hands of a fourth party. The role of the controller is to fabricate an 8-qubit entangled state and distribute the respective qubits involved in the entangled state to the relevant parties and thereby creating a noisy quantum channel. The protocol is first ideally discussed in the noise-free case which is then a perfect joint remote state preparation protocol with fidelity 1. Then, we discuss the performance of the protocol in the presence of noise in which the fidelity is diminished. We consider three different types of noises and analyze the variation of fidelity of the process.
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.
Using two tripartite Greenberger—Horne—Zeilinger (GHZ) states as the shared channels, we investigate the noise effects on the deterministic joint remote preparation of an arbitrary two-qubit state. By unitary matrix decomposition procedure, we first construct the quantum logic circuit of the deterministic joint remote state preparation protocol. Then, we analytically derive the fidelity and the average fidelity for the deterministic joint remote preparation of an arbitrary two-qubit state and of four types of special two-qubit states under the influence of the Pauli noises. It is found that the fidelity depends on the noise types, the qubit-environment coupling strength, and the state to be remotely prepared. Moreover, even if the two GHZ channels are subject to the same environmental noises, the average fidelities for remotely preparing different two-qubit states display different time evolution behaviors. The remote preparation of the identical two-qubit states also shows that the average fidelities affected by different noisy environments exhibit different evolution actions.
A scheme is proposed for the remote preparation of a two qubit quantum state by using two nonmaximally entangled states as the quantum channel. The effects of the environment noise on the quantum channels are considered, in which the time-evolution is ruled by the master equations of the density matrices in the Lindblad form. We investi- gated the influence of environment noise on the fidelity of the remote state preparation based on three types of quantum channels. It is found that the output state of remote state preparation, as time goes on, has a higher fidelity in the case of the quantum channel consists of |01> and |10> basis than that of |00> and |11> basis. Furthermore, the results also demonstrate that the fidelity is proportional to the product of both situations above when the channel consists of the mixture basis, and its value is between of them.