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Acta Physica Sinica

Influence of decoherence of entanglement on deterministic remote state preparation

Guo Zhen, Yan Lian-Shan, Wei Pan, Luo Bin, Mingfeng Xu

Published Jan 1, 2011• 5 citations
Publisher

Abstract

We investigate the influence of decoherence of entanglement on the deterministic remote state preparation. Firstly, the determinability and the depletion of entanglement bits and classical bits are obtained. Then two kinds of decoherent channels (depolarizing and dephasing) are analyzed. For the depolarizing channel, the fidelity is related only to the depolarization and the latitude of target quantum bits on the Bloch sphere, but is independent of longitude. For the dephasing channel, the fidelity is not affected by the quantum channel and only related to the latitude of target quantum bits.

DOI
10.7498/aps.60.060301

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We investigate the influence of decoherence of entanglement on the deterministic remote state preparation. Firstly, the determinability and the depletion of entanglement bits and classical bits are obtained. Then two kinds of decoherent channels (depolarizing and dephasing) are analyzed. For the depolarizing channel, the fidelity is related only to the depolarization and the latitude of target quantum bits on the Bloch sphere, but is independent of longitude. For the dephasing channel, the fidelity is not affected by the quantum channel and only related to the latitude of target quantum bits.
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In this paper,we propose a scheme in which one can realize remote state preparation(RSP) of an entangled state through entanglement swapping.In ideal conditions where quantum systems about RSP do not suffer unwanted interactions with the outside environment,two two-particle entangled states are used as quantum channels to remotely prepare an entangled state.Furthermore,we investigate RSP of an entangled state through noisy channels.Studies show the fidelity of the process of RSP is different under influences of different types of noises.We also investigate the influence of decoherence rate on remote state preparation for a deterministic state.
We investigate the influence of a noisy environment on the remote preparation of the multi-qubit equatorial state, and specifically deduce the final states and fidelities of the remote preparation of the three-qubit and four-qubit equatorial states under diverse types of noisy environments, namely, amplitude damping, bit flip, phase damping, phase flip, bit-phase flip, depolarization, and non-Markov environments. The results show that when the decoherence factors of the front six noises are equal, the influence degrees of phase damped noise, bit flip noise, phase flip noise, and bit-phase flip noise are similar, while the information loss caused by the amplitude damped noise and depolarizing noise is less. In particular, the bit flip noise and depolarizing noise may have more complex effects on the remote state preparation (RSP) schemes depending on the phase information of the target states, even for the ideal cases where the fidelity values are always 1 for specific phase relations. In the non-Markov environment, owing to the back and forth of information between the environment and systems, fidelities exhibit oscillating behavior and the minimum value may stay greater than zero for a long evolutionary time. These results are expected to have potential applications for understanding and avoiding the influence of noise on remote quantum communication and quantum networks.
Using a quantum channel consisting of a GHZ state exposed to noisy environment, we investigate how to remotely prepare an entangled state and a qubit state, respectively. By solving the master equation in the Lindblad form, the influence of the various types of noises on the GHZ state is first discussed. Then we use the fidelity to describe how close the remotely prepared state and the initial state are. Our results show that the fidelity is a function of the decoherence rates and the angles of the initial state. It is found that for each of the two RSP schemes, the influence of the noise acting simultaneously in x, y, and z directions on the average fidelity is the strongest while the influence of the noise acting in x or z direction on the average fidelity is relatively weaker.
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In this paper, the theoretical investigation of remote preparation of an entangled state is studied in nonideal conditions. Our studies include two parts. In the first part, we consider the remote state preparation (RSP) of an entangled state through two equally noisy quantum channel states, namely, a mixture of Bell states. Studies show there is a particular mixed-state channel for which all pure entangled states remain entangled after this inexact RSP. In the second part, we suppose that noises which quantum channels suffer from can be expressed as the Lindblad operators. The master equation of the system can be expressed in the Lindblad form. Through solving the master equation, we calculate the fidelity as a function of decoherence rates and parameters of the state to be prepared. For a given entangled state, we investigate the influence of different types of noises on the fidelity.