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Chinese Physics B

Deterministic joint remote preparation of an arbitrary two-qubit state in the presence of noise

Zhongfang Chen, Jin‐Ming Liu, Лей Ма

Published Feb 1, 2014• 26 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/23/2/020312

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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.
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.
Using a GHZ-class state as a quantum channel, we investigate the remote preparation of a qubit state and that of an entangled state in noisy environments. By analytically solving the master equation in Lindblad form, we first obtain the time evolution of the GHZ-class quantum channel. Then the influence of the noises on the process of remote state preparation is considered through analytical derivation of the fidelity and numerical calculations of the corresponding average fidelity. Our results show that the fidelity depends on the noise type, the state to be remotely prepared, the GHZ-class state and the decoherence rate. Moreover, it is found that no matter whether the qubit state or the entangled state is to be remotely prepared, the maximally entangled quantum channel has a relatively stronger ability to resist the influence of noises. Besides, the effect of the bit–phase flip noise on the average fidelity is relatively stronger than that of the bit flip noise or phase flip noise.
The effect of noise on the transmission of quantum state has attached much interest recently. Here we investigate the effect of different types of quantum noise on deterministic exact remote preparation of an arbitrary single-qubit state. Four types of noise which usually encountered in application of quantum remote state preparation, including bit-flipping, phase-flipping, depolarizing and amplitude damping, are considered. The average fidelities of remote state preparation for any combinations of noise are calculated. It is shown that more fidelity can be achieved via less entanglement in single-qubit remote preparation when part or all of the entangled qubits are subjected to amplitude damping noise. It is shown that in several situations more noise may leading to more fidelity in remote state preparation. Moreover, we discuss the effect of noise on probabilistic remote state preparation.
We present a protocol for remote preparation of an arbitrary two-qudit state by using a four-qudit [Formula: see text]-type state as the quantum channel via positive operator-valued measurement. We first propose the protocol for remote preparation of an arbitrary two-qudit state via positive operator-valued measurement in noiseless environment and then discuss the protocol in noisy environments. Four important quantum decoherence noise models, the dephasing noise, the qudit-flip noise, the qudit-phase-flip noise and the depolarizing noise, are considered in our protocol. The output states and the fidelities of remote state preparation in four different types of quantum noises are presented. It is shown the protocol for remote state preparation via positive operator-valued measurement with [Formula: see text]-type state has the advantage of transmitting less particles for remote preparing an arbitrary two-qudit state. The fidelities of remote state preparation depend on the coefficients of original two-qudit state and the decoherence rates of the noise models.
Abstract It is a significant subject to explore effective quantum communication protocol and enhance the efficiency of the transmission process in noisy environments. In this paper, we investigate the bidirectional controlled remote preparation of an arbitrary single-qubit state in the presence of dissipative environments by using two EPR states as the entanglement source. We first construct the quantum circuit of our scheme by means of unitary matrix decomposition procedure, then the effects of the Markovian and non-Markovian environmental noises acting on the EPR states are considered through the analytical derivation and numerical calculations of the corresponding average fidelity. Moreover, we adopt two methods of weak measurement reversal (WMR) and detuning modulation to improve the average fidelity. Our results show that the average fidelity can be remarkably enhanced under appropriate conditions of the WMR strength and the detuning. Compared with the average fidelity behaviors in dissipative environments, it is also shown that the two methods for fidelity improvement are more efficient in the non-Markovian regime than in the Markovian regime.