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arXiv:1903.03359 · npj Quantum Information

Detecting non-Markovianity via quantified coherence: theory and experiments

Kang‐Da Wu, Zhibo Hou, Guo‐Yong Xiang, Chuan‐Feng Li, Guang‐Can Guo, Daoyi Dong, Franco Nori

Published Jun 19, 2020• 50 citations
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Abstract

Abstract The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the quantum-incoherent relative entropy of coherence ( $${\mathcal{Q}}{\mathcal{I}}$$ QI REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the $${\mathcal{Q}}{\mathcal{I}}$$ QI REC. Also we implement an all-optical experiment to demonstrate that the behavior of the $${\mathcal{Q}}{\mathcal{I}}$$ QI REC is coincident with the entanglement shared between the system and the ancilla for both Markovian and non-Markovian evolution; while other coherence-based non-Markovian information carriers violate monotonicity, even in Markovian processes. Moreover, both theoretically and experimentally, we show that non-Markovianity enhances the ability of creating coherence on an ancilla. This is the first experimental study of the relation between dynamical behavior of the $${\mathcal{Q}}{\mathcal{I}}$$ QI REC and the phenomenon of information backflow. Our methods for detecting non-Markovianity are applicable to general quantum evolutions.

DOI
10.1038/s41534-020-0283-3

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Abstract The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the quantum-incoherent relative entropy of coherence ( QI{\mathcal{Q}}{\mathcal{I}}QI QI REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the QI{\mathcal{Q}}{\mathcal{I}}QI QI REC. Also we implement an all-optical experiment to demonstrate that the behavior of the QI{\mathcal{Q}}{\mathcal{I}}QI QI REC is coincident with the entanglement shared between the system and the ancilla for both Markovian and non-Markovian evolution; while other coherence-based non-Markovian information carriers violate monotonicity, even in Markovian processes. Moreover, both theoretically and experimentally, we show that non-Markovianity enhances the ability of creating coherence on an ancilla. This is the first experimental study of the relation between dynamical behavior of the QI{\mathcal{Q}}{\mathcal{I}}QI QI REC and the phenomenon of information backflow. Our methods for detecting non-Markovianity are applicable to general quantum evolutions.
Abstract Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e. the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on l 1 norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative entropy of coherence are more comfortable than the original Tsallis relative entropy of coherence for small .
In this paper, we use coherence measures based on the Tsallis relative α entropies (coherence α measures), with 0<α≤2, to detect the non-Markovianity of incoherent completely positive dynamical maps. At first, in a typical open quantum system, we study the differences between these quantum coherence (QC) measures (with different α) in reveling the non-Markovianity and meanwhile, we compare our results with the ones in Neto et al. (2016). We conclude that coherence α measures can detect non-Markovianity better than non-Markovianity measure which is based on entanglement. Then, in another example, we compare coherence α measures (with different α) with two other non-Markovianity criteria (trace distance and mutual information based criteria). The results show that generally, the coherence α measures can detect non-Markovianity at least as well as the two other criteria.
The dynamical role of system-environment correlations will lead to the violation of Landauer's principle and may result in a non-Markovian dynamics of the system. Here, we employ entropic quantities called the telescopic relative entropy, to detect non-Markovianity [N. Megier, Phys. Rev. Lett. 127, 030401 (2021)], and study the relation between information backflow of non-Markovian dynamics and the validity of Landauer's principle. We consider a class of energy-conserving system-environment interactions in qubit systems, and we prove that the violation of Landauer's principle corresponds to information backflow of a thermalizing process without coherence and vice versa. Then we study the effect of quantum coherence of the system on the relationship between non-Markovianity and Landauer's principle, and we find that coherence will break the corresponding relation in the information backflow and violation of Landauer's principle. Based on this, we explain the physical mechanism of non-Markovianity in this irreversible process of heat dissipation and information erasure. We further numerically confirm the above theoretical results by means of a collision model.
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.
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.
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamio\l{}kowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.