Phase space measures of information flow in open systems: A quantum and classical perspective of non-Markovianity
arXiv:2409.08749 · doi:10.1103/PhysRevA.110.062401
Abstract
The exchange of information between an open quantum system and its environment, especially the backflow of information from the environment to the open system associated with quantum notions of non-Markovianity, is a widely discussed topic for years now. This information flow can be quantified by means of the trace distance of pairs of quantum states which provides a measure for the distinguishability of the states. The same idea can also be used to characterize the information flow in classical open systems through a suitable distance measure for their probability distributions on phase space. Here, we investigate the connection between the trace distance based quantum measure and the Kolmogorov distance for differently ordered quasi-probability distributions on phase space. In particular, we show that for any pair of quantum states one can find a unique quasi-probability distribution for which the Kolmogorov distance coincides with the trace distance. We further study the quantum-to-classical transition of the distance measures. Employing the Caldeira-Legget model of quantum Brownian motion as a prototypical example, numerical simulations indicate a particularly rapid convergence of the Kolmogorov distance of the Wigner functions to the trace distance in the classical uncertainty limit, which establishes the Wigner function distance as an optimal tool for measuring semi-classical information backflow and for quantifying non-Markovianity in open continuous variable quantum systems.
References in corpus (24)
- Decoherence, einselection, and the quantum origins of the classical
- Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
- Non-Markovian dynamics in open quantum systems
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Continuous variable quantum information: Gaussian states and beyond
- Measure for the Non-Markovianity of Quantum Processes
- Quantum Decoherence
- Irreversible entropy production, from quantum to classical
- Concepts of quantum non-Markovianity: a hierarchy
- On measures of non-Markovianity: divisibility vs. backflow of information
- Markovian and non-Markovian dynamics in quantum and classical systems
- Optimal state pairs for non-Markovian quantum dynamics
- Witness for initial system-environment correlations in open system dynamics
- Generalized trace distance measure connecting quantum and classical non-Markovianity
- Quantification of memory effects in the spin-boson model
- Collision models in open system dynamics: A versatile tool for deeper insights?
- Entropic bounds on information backflow
- Non-Markovian effects in the spin-boson model at zero temperature
- Non-Markovianity of Quantum Brownian Motion
- Entropic and trace distance based measures of non-Markovianity
- Holevo skew divergence for the characterization of information backflow
- Kernel-based quantum regressor models learn non-Markovianity
- Signatures of non-Markovianity in classical single-time probability distributions
- Witnessing non-Markovianity by Quantum Quasi-Probability Distributions