Classical quantum stochastic processes

Abstract

We investigate the role of coherence and Markovianity in finding an answer to the question whether the outcomes of a projectively measured quantum stochastic process are compatible with a classical stochastic process. For this purpose we put forward an operationally motivated definition of incoherent dynamics applicable to any open system's dynamics. For non-degenerate observables described by rank-1 projective measurements we show that classicality always implies incoherent dynamics, whereas the converse is only true for invertible Markovian (but not necessarily time-homogeneous) dynamics. For degenerate observables the picture is somewhat reversed as classicality does no longer suffice to imply incoherent dynamics (even in the invertible Markovian case), while an incoherent, invertible Markovian dynamics still implies classicality.

4 + 3 pages incl. 1 Figuere and References. Slightly upgraded and final version

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Cited by in corpus (43)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Demonstration of non-Markovian process characterisation and control on a quantum processor
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• When is a non-Markovian quantum process classical?
• Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories
• An operational approach to quantum stochastic thermodynamics
• Tensor network based machine learning of non-Markovian quantum processes
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Classicality, Markovianity and local detailed balance from pure state dynamics
• Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach
• 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
• Accessible coherence in open quantum system dynamics
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Einselection, Equilibrium and Cosmology
• Equilibration of Multitime Quantum Processes in Finite Time Intervals
• On the sampling complexity of open quantum systems
• Experimental Control of the Degree of Non-Classicality via Quantum Coherence
• Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics
• Objectivity of classical quantum stochastic processes
• Quantum Markov monogamy inequalities
• Capturing long-range memory structures with tree-geometry process tensors
• Hidden Quantum Memory: Is Memory There When Somebody Looks?
• Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system
• Classical-quantum correspondence in the noise-based dissipative systems
• Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics
• Decoherence of Histories: Chaotic Versus Integrable Systems
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory
• Superclassical non-Markovian open quantum dynamics
• Classical Invasive Description of Informationally-Complete Quantum Processes
• Purely quantum memory in closed systems observed via imperfect measurements
• Leggett-Garg inequalities for multitime processes
• Temporal nonclassicality in continuous-time quantum walks
• Quantum non-Markovianity elusive to interventions
• Phenomenological quantum mechanics: I. Phenomenology of quantum observables
• Toy Model Challenging Prevailing Definitions of Classicality
• Diagnosing chaos with projected ensembles of process tensors
• Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables
• Connecting Commutativity and Classicality for Multi-Time Quantum Processes