Almost Markovian processes from closed dynamics

Abstract

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should be the norm, the ubiquity of Markovian processes is undeniable. Here, without resorting to the Born-Markov assumption of weak coupling or making any approximations, we formally prove that processes are close to Markovian ones, when the subsystem is sufficiently small compared to the remainder of the composite, with a probability that tends to unity exponentially in the size of the latter. We also show that, for a fixed global system size, it may not be possible to neglect non-Markovian effects when the process is allowed to continue for long enough. However, detecting non-Markovianity for such processes would usually require non-trivial entangling resources. Our results have foundational importance, as they give birth to almost Markovian processes from composite closed dynamics, and to obtain them we introduce a new notion of equilibration that is far stronger than the conventional one and show that this stronger equilibration is attained.

arXiv comment9 pages, 13 pages of appendices, 5 figures, numerical example. Replaced with journal version and fixed hyperlinks

References in corpus (40)

• Average Entropy of a Subsystem
• Non-Markovian dynamics in open quantum systems
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• The role of quantum information in thermodynamics --- a topical review
• Distance measures to compare real and ideal quantum processes
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• The approach to thermal equilibrium in quantized chaotic systems
• Theoretical framework for quantum networks
• Chaos and complexity by design
• Quantum Circuits Architecture
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Local random quantum circuits are approximate polynomial-designs
• Operational Markov condition for quantum processes
• Absence of Thermalization in Nonintegrable Systems
• Quantum causal modelling
• Chaos, Complexity, and Random Matrices
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Quantum equilibration in finite time
• How to generate random matrices from the classical compact groups
• Entangling power of the quantum baker's map
• Collision models in quantum optics
• Operational approach to open dynamics and quantifying initial correlations
• Efficient unitary designs with nearly time-independent Hamiltonian dynamics
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• Equilibration time scales of physically relevant observables
• An introduction to operational quantum dynamics
• Symbolic integration with respect to the Haar measure on the unitary group
• The complexity of energy eigenstates as a mechanism for equilibration
• Large Deviation Bounds for k-designs
• Tomographically reconstructed master equations for any open quantum dynamics
• Distinguishing decoherence from alternative quantum theories by dynamical decoupling
• Thermalization under randomized local Hamiltonians
• Quantum Speed Limits for Quantum Information Processing Tasks
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Statistical distribution of the local purity in a large quantum system
• Matrix integrals over unitary groups: An application of Schur-Weyl duality
• Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
• Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state
• Weingarten Calculus and the IntHaar Package for Integrals over Compact Matrix Groups

Cited by in corpus (32)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Classicality, Markovianity and local detailed balance from pure state dynamics
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Randomized benchmarking for non-Markovian noise
• Exponential improvement for quantum cooling through finite-memory effects
• Markovianization with approximate unitary designs
• Non-Markovian Memory Strength Bounds Quantum Process Recoverability
• Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
• Relaxation of Multitime Statistics in Quantum Systems
• First Principles Numerical Demonstration of Emergent Decoherent Histories
• Signatures of quantum chaos in an out-of-time-order tensor
• Equilibration of Multitime Quantum Processes in Finite Time Intervals
• Quantifying non-Markovianity via conditional mutual information
• On the sampling complexity of open quantum systems
• Equilibration on average in quantum processes with finite temporal resolution
• Modern Concepts of Quantum Equilibration Do Not Rule Out Strange Relaxation Dynamics
• Memory Effects in Quantum Processes
• Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Capturing long-range memory structures with tree-geometry process tensors
• Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Non-Markovianity of subsystem dynamics in isolated quantum many-body systems
• On the relation between quantum Darwinism and approximate quantum Markovianity
• Process tensor distinguishability measures
• George Sudarshan and Quantum Dynamics
• Purely quantum memory in closed systems observed via imperfect measurements
• Learning the non-Markovian features of subsystem dynamics
• Equilibration and Typicality in Quantum Processes
• Toy Model Challenging Prevailing Definitions of Classicality
• Diagnosing chaos with projected ensembles of process tensors