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Journal of Physics A Mathematical and General

Decoherence of quantum information in the non-Markovian qubit channel

Masashi Ban, Sachiko Kitajima, Fumiaki Shibata

Published Jul 27, 2005• 38 citations
Publisher

Abstract

Decoherence of quantum information of qubits is investigated under the influence of the non-Markovian quantum channel, where the correlation time of reservoir variables takes a finite value. Degradation of purity, distinguishability and entanglement of qubit states are evaluated. It is found that the non-Markov effect makes the coherence time of quantum information longer than that obtained for the Markovian quantum channel. Furthermore, the quantum teleportation and quantum dense coding of qubits are considered under the influence of non-Markov channels. The fidelity between teleported and original states and the Holevo capacity are obtained.

DOI
10.1088/0305-4470/38/32/006

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Decoherence of quantum information of qubits is investigated under the influence of the non-Markovian quantum channel, where the correlation time of reservoir variables takes a finite value. Degradation of purity, distinguishability and entanglement of qubit states are evaluated. It is found that the non-Markov effect makes the coherence time of quantum information longer than that obtained for the Markovian quantum channel. Furthermore, the quantum teleportation and quantum dense coding of qubits are considered under the influence of non-Markov channels. The fidelity between teleported and original states and the Holevo capacity are obtained.
Decoherence of quantum information carried by single-mode and two-mode Gaussian states is investigated under the influence of non-Markovian quantum channels, where correlation times of reservoir variables are assumed to take finite values. Degradation of purity, distinguishability and non-classicality of single-mode Gaussian states and relaxation of entanglement of two-mode Gaussian states are examined. The results show the importance of the non-Markovian effect of a thermal reservoir. Furthermore, continuous variable quantum teleportation is considered when a sender and a receiver share a two-mode Gaussian state through non-Markovian quantum channels.
Decoherence of entanglement of qubits is investigated which is caused by the phenomenological quantum channel (the Bloch channel) equivalent to the Bloch equations. It is shown how the decoherence of entanglement depends on the longitudinal and transverse relaxation times and the equilibrium value of the qubit. The quantum dense coding system under the influence of the Bloch channel is also investigated. The Shannon mutual information obtained by the Bell measurement and the Holevo capacity is calculated. Furthermore, the microscopic system-reservoir model which yields the Bloch equations is considered. The result shows that the temperature of the thermal reservoir significantly affects the decoherence of entanglement.
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
We investigate the fidelity and the linear entropy of teleportation using a shared two qubit initially maximally entangled state as a quantum channel, in which one qubit interacts with a two-state system named as the probe particle in a reservoir by dispersive atom-field coupling. Without the coupling of the probe particle with the reservoir, the quantum channel state is a pure state but not an initially maximally entangled state under the influence of the probe particle, and thus Bob obtains a pure state with an average fidelity fluctuating between 2/3 and 1 with time t. In the cases of the probe particle coupling with the reservoir the Markovian and non-Markovian dynamics of such a quantum channel are discussed in detail to show the influence of the reservoir on teleportation. The quantum channel state is a mixed state, but its entanglement does not die under the influence of the reservoir. It is found that, for a given teleported state, the fidelity and the linear entropy both evolve asymptotically to their fixed values, respectively, which are relative to the decay rate γ (Markovian) or to the pseudomode decay rate Γ (non-Markovian). Furthermore, when time t ≫ γ^(-1) and t ≫ Γ^(-1), the average fidelity increases with the augments of γ and Γ, while it decreases with the aggrandizement of the dispersive interaction strength κ.
We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a single-mode cavity, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.
We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a cavity field whether the system is closed or open, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.