Quantum non-Markovian processes break conditional past-future independence

Abstract

For classical Markovian stochastic systems, past and future events become statistically independent when conditioned to a given state at the present time. Memory non-Markovian effects break this condition, inducing a non-vanishing conditional past-future correlation. Here, this classical memory indicator is extended to a quantum regime, which provides an operational definition of quantum non-Markovianity based on a minimal set of three time-ordered quantum system measurements and post-selection. The detection of memory effects through the measurement scheme is univocally related to departures from Born-Markov and white noise approximations in quantum and classical environments respectively.

arXiv comment5 pages, 2 figures, and supplemental material. To be published in Phys.Rev. Lett

References in corpus (37)

• 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
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Assessing non-Markovian dynamics
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Canonical form of master equations and characterization of non-Markovianity
• On the degree of non-Markovianity of quantum evolution
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Operational Markov condition for quantum processes
• On measures of non-Markovianity: divisibility vs. backflow of information
• Geometrical characterization of non-Markovianity
• Decoherence from spin environments
• Gaussian Decoherence from Random Spin Environments
• Non-Markovianity through accessible information
• Past quantum states
• Comparative study of non-Markovianity measures in exactly solvable one and two qubit models
• Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
• Comparing different non-Markovianity measures: A case study
• Time-Symmetric Quantum Theory of Smoothing
• Prediction and retrodiction for a continuously monitored superconducting qubit
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Observing interferences between past and future quantum states in resonance fluorescence
• Lindblad rate equations
• Random Lindblad equations from complex environments
• Quantum State Smoothing
• Master Equation for Retrodiction of Quantum Communication Signals
• Quantum retrodiction in open systems
• Non-Markovian non-stationary completely positive open quantum system dynamics
• Correlations of the time dependent signal and the state of a continuously monitored quantum system
• Quantum instruments as a foundation for both states and observables
• Homodyne monitoring of post-selected decay
• Maximally non-Markovian quantum dynamics without environment backflow of information
• Past observable dynamics of a continuously monitored qubit
• Smoothed quantum-classical states in time-irreversible hybrid dynamics
• Entropic relations for retrodicted quantum measurements

Cited by in corpus (33)

• Machine learning non-Markovian quantum dynamics
• Conditional past-future correlation induced by non-Markovian dephasing reservoirs
• Quantum non-Markovianity: Overview and recent developments
• Detection of quantum non-Markovianity close to the Born-Markov approximation
• Unifying theory of quantum state estimation using past and future information
• Entropic and trace distance based measures of non-Markovianity
• Quantum regression beyond the Born-Markov approximation for generalized spin-boson models
• Enhancing quantum transport efficiency by tuning non-Markovian dephasing
• Non-Markovianity, information backflow and system-environment correlation for open-quantum-system processes
• Holevo skew divergence for the characterization of information backflow
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Decoherence-Free Rotational Degrees of Freedom for Quantum Applications
• On Markovianity and classicality in multilevel spin-boson models
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Interferometric Approach to Open Quantum Systems and Non-Markovian Dynamics
• Quantum causal correlations and non-Markovianity of quantum evolution
• Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics
• Perturbation theory for operational quantum non-Markovianity
• Detection of Bidirectional System-Environment Information Exchanges
• Measuring non-Markovianity via incoherent mixing with Markovian dynamics
• A solvable class of non-Markovian quantum multipartite dynamics
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space
• Memory effects in multipartite systems coupled by non-diagonal dephasing mechanisms
• Quantifying environment non-classicality in dissipative open quantum dynamics
• Quantum non-Markovian "casual bystander" environments
• On the non-Markovianity of quantum semi-Markov processes
• On the eternal non-Markovianity of non-unital quantum channels
• Quantum state smoothing cannot be assumed classical even when the filtering and retrofiltering are classical
• Superclassical non-Markovian open quantum dynamics
• Violation of Diagonal Non-Invasiveness: A Hallmark of Non-Classical Memory Effects
• Efficient and operational quantifier of non-divisibility in terms of channel discrimination
• Non-Markovianity-based ultrasensitive parameter estimation
• Geometric signature of non-Markovian dynamics