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arXiv:1111.5967 · Journal of Physics B Atomic Molecular and Optical Physics

Teleportation of the one-qubit state in decoherence environments

Ming-Liang Hu

Published Jan 12, 2011• 20 citations
arXivHTMLPDF

Abstract

We study standard quantum teleportation of a one-qubit state for the situation in which the channel is subject to decoherence, and where the evolution of the channel state is ruled by a master equation in the Lindblad form. A detailed calculation reveals that the quality of teleportation is determined by both the entanglement and the purity of the channel state, and only the optimal matching of them ensures the highest fidelity of standard quantum teleportation. Also our results demonstrated that the decoherence induces distortion of the Bloch sphere for the output state with different rates in different directions, which implies that different input states will be teleported with different fidelities.

DOI
10.1088/0953-4075/44/2/025502

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We study standard quantum teleportation of a one-qubit state for the situation in which the channel is subject to decoherence, and where the evolution of the channel state is ruled by a master equation in the Lindblad form. A detailed calculation reveals that the quality of teleportation is determined by both the entanglement and the purity of the channel state, and only the optimal matching of them ensures the highest fidelity of standard quantum teleportation. Also our results demonstrated that the decoherence induces distortion of the Bloch sphere for the output state with different rates in different directions, which implies that different input states will be teleported with different fidelities.
We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noises acting on quantum channels. If the quantum channels are subject to isotropic noise, the average fidelity decays to 1/2,1/2,1/2, which is smaller than the best possible value of 2/32/32/3 obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than 2/3.2/3.2/3.
We investigate quantum teleportation of a single unknown qubit state for the dissipative situation in which both qubits of the entangled channels that are formed by the pure and mixed maximally entangled states are subjected to local structured reservoirs. We consider the dissipative factors in Markovian and non-Markovian regimes on the average fidelity of the teleportation by solving the quantum master equation. It is shown that the fidelity of teleportation decreases exponentially over time in Markovian environments and attenuates oscillatorily in non-Markovian ones. In addition, when the non-Markovian and detuning conditions are satisfied simultaneously, the fidelity increases as the detuning increases. Even with a lower purity of entanglement, fidelity can be preserved effectively at comparatively high levels.
We study an entangled two-mode coherent state within the framework of2×2-dimensional Hilbert space. We investigate the problem of quantum teleportation ofa superposition coherent state via an entangled coherent channel. By three differentmeasures with the titles ``minimum assured fidelity (MASF)”, ``average teleportationfidelity” and ``optimal fidelity (f)” we study the quality of this kind of teleportation.Decoherence properties of the entangled coherent state due to channel losses areanalysed. For a symmetric noise channel, the degradation of optimal fidelity and degreeof entanglement are calculated. Also by two different measures with the titles``concurrence” and ``entanglement of formation” we study the amount of entanglementof a decohered quantum channel and discuss its details. We demonstrate thatentanglement of the decohered entangled coherent state is reduced but not throughlylost. Finally we find that the optimal fidelity of the decohered entangled coherent state ismore than the classical limit and the decohered entangled coherent state may be usefulfor quantum teleportation.
We study bidirectional teleportation while explicitly taking into account a mixed environment. This environment initially causes pure dephasing decoherence of the Bell state which assists teleportation. We find that when teleportation is performed in one direction it is accompanied by a transfer of correlations into the teleported qubit state. In the other direction, if no new decoherence process occurs then not only the state of the qubit, but also its correlations with the environment are teleported with unit fidelity. These processes do not depend on the measurement outcome during teleportation and do not differentiate between classical and quantum decoherence. If, on the other hand, the second teleportation step is preceded by decoherence of the Bell state then the situation is much more complicated. Teleportation and transfer of correlations occur simultaneously, yielding different teleported qubit-environment states for different measurement outcomes. These states can differ in the degree of coherence of the teleported qubit, but only for an entangling Bell-state-environment interaction in the first step can they have different amounts of qubit-environment entanglement. In the extreme case, one of the teleported qubit states can be entangled with the environment while the other is separable.
Quantum teleportation plays a significant role in the field of quantum communication. This paper investigates quantum teleportation through a noisy environment by using GHZ state and non-standard W state as quantum channels. We analyze the efficiency of quantum teleportation by solving analytically a master equation in Lindblad form. Following the quantum teleportation protocol, we obtain the fidelity of quantum teleportation as a function of evolution time. The calculation results show that the teleportation fidelity using non-standard W is higher in comparison to GHZ state at the same evolution time. Moreover, we consider the efficiency of teleportation with weak measurements and reverse quantum measurement under amplitude damping noise. Our analysis suggests that the teleportation fidelity using non-standard W is also more robust to noise than GHZ state in the same conditions. Interestingly, we found that weak measurement and its reverse operation have no positive effect on the efficiency of quantum teleportation by using GHZ and non-standard W state in the amplitude damping noise environment. In addition, we also demonstrate the efficiency of quantum teleportation can be improved by making minor modifications to the protocol.
Abstract This study discusses the one-way quantum teleportation of 2 qubits through a 4-qubit Bell state channel that is subject to decoherence. Decoherence is one of the unavoidable effects of noise in the transmission process. In the case of quantum teleportation, noise has an impact on the channel, causing changes in its state due to noise. In the absence of noise, teleportation occurs in an ideal state, resulting in a fidelity value of 1, signifying successful information transfer in the ideal scenario. However, when examined in the presence of noise, fidelity is not equal to 1 due to the influence of noise factors and the coefficient of the transmitted state. These noise factors indicate the strength of the noise. The stronger the noise, the lower the fidelity becomes.