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Physical Review A

Information trapping in quantum communications

Seyed Mohammad Hosseiny, Jamileh Seyed‐Yazdi, Milad Norouzi

Published Sep 6, 2024• 6 citations
Publisher

Abstract

Many quantum systems display Markovian and non-Markovian behaviors with the information flow and backflow between the system and the surrounding environment. In this paper, we introduce a definition of the dynamics of open quantum systems called information trapping, which is a special case of the information flow. We show that under specific conditions, the information flow can exhibit behavior beyond Markovian or non-Markovian system dynamics. The physical reason behind this phenomenon may arise from the entanglement between the system and the environment, such that the rates of entangling and disentangling can equalize over time, influenced by the quantum memory of the system and environmental decoherence effects. This proposal is investigated by considering some witnesses of the behavior of the system dynamics such as fidelity, trace distance, the Holevo quantity, and Hilbert-Schmidt speed in the quantum teleportation and dense coding protocols based on the open quantum system consisting of an $XXZ$ chain Heisenberg affected by intrinsic decoherence. The main achievement of this work is focused on facilitating access to faithful quantum communication.

DOI
10.1103/physreva.110.032608

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Many quantum systems display Markovian and non-Markovian behaviors with the information flow and backflow between the system and the surrounding environment. In this paper, we introduce a definition of the dynamics of open quantum systems called information trapping, which is a special case of the information flow. We show that under specific conditions, the information flow can exhibit behavior beyond Markovian or non-Markovian system dynamics. The physical reason behind this phenomenon may arise from the entanglement between the system and the environment, such that the rates of entangling and disentangling can equalize over time, influenced by the quantum memory of the system and environmental decoherence effects. This proposal is investigated by considering some witnesses of the behavior of the system dynamics such as fidelity, trace distance, the Holevo quantity, and Hilbert-Schmidt speed in the quantum teleportation and dense coding protocols based on the open quantum system consisting of an XXZXXZXXZ chain Heisenberg affected by intrinsic decoherence. The main achievement of this work is focused on facilitating access to faithful quantum communication.
Exchange of information between a quantum system and its surrounding environment plays a fundamental role in the study of the dynamics of open quantum systems. Here we discuss the role of the information exchange in the non-Markovian behavior of dynamical quantum processes following the decoherence approach, where we consider a quantum system that is initially correlated with its measurement apparatus, which in turn interacts with the environment. We introduce a way of looking at the information exchange between the system and environment using the quantum loss, which is shown to be closely related to the measure of non-Markovianity based on the quantum mutual information. We also extend the results of Fanchini et al. [Phys. Rev. Lett. 112, 210402 (2014)] in several directions, providing a more detailed investigation of the use of the accessible information for quantifying the backflow of information from the environment to the system. Moreover, we reveal a clear conceptual relation between the entanglement- and mutual-information-based measures of non-Markovianity in terms of the quantum loss and accessible information. We compare different ways of studying the information flow in two theoretical examples. We also present experimental results on the investigation of the quantum loss and accessible information for a two-level system undergoing a zero temperature amplitude damping process. We use an optical approach that allows full access to the state of the environment.
The dynamics of an open quantum system is non-Markovian when memory effect is non-negligible. The quantum memory effect is a very complex issue and presently there is no universally accepted method to quantify it. By examining the memory kernel of the Nakajima-Zwanzig master equation, we study the memory effect in a theoretical model consisting of a spin coupled to an environment of an Ising spin chain subject to a transverse field. We find that it can be dictated by either the time correlation in the environment, or the system-environment correlation, depending on the strength of the transverse field and the state of the environment. We analyze the information loss to the environment and backflow from it, and discover that the information flow is not always a reliable indicator for the nature of the dynamics.
The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.
Abstract Quantum entanglement is a special nonlocal association between quantum systems. It is a fundamental feature of the difference between quantum and classical. At the same time, it acts as a very important resource in quantum informatics. Therefore, entanglement plays a noble role in quantum information and quantum computing. Quantum dense coding, as an application of quantum entanglement in practice, is a quantum communication protocol characterized by security and secrecy, which plays a very important role in quantum informatics and cryptography. This paper is mainly in the Non-Markovian environment of Heisenberg Spin chain system, using the quantum dense coding scheme proposed by Bennett et al. to study The dynamics of quantum dense coding channel capacity evolution with time and the entanglement dynamics of the system are discussed in detail.Based on the theoretical knowledge of open quantum systems and the maximum entangled state ∣ψAB⟩=12(∣11⟩+∣00⟩)\left| {{{\mathbf{\psi }}_{{\mathbf{AB}}}}} \right\rangle =\frac{1}{{\sqrt 2 }}\left( {\left| {11} \right\rangle +\left| {00} \right\rangle } \right)∣ψAB​⟩=2​1​(∣11⟩+∣00⟩) as the initial state, the density matrix of the system evolution over time is obtained by quantum state diffusion method,and the evolution of channel capacity and entanglement over time of Heisenberg spin chains is simulated accurately. The results show that: the capacity and entanglement of dense coded channel oscillate with time and reach different stable values. Environmental correlation coefficientγ\gammaγand coupling strengthη\etaηand a play an important role in dense coding and quantum entanglement of quantum systems.Proper selection of parameters can keep the system good entanglement characteristics and increase the channel capacityχ\chiχof the system, thus ensuring the effective transmission and processing of quantum information in practice. It lays a solid foundation for quantum computing
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.
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.