Quantum Markov Order

Abstract

We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the appropriate limit: when the stochastic process is classical and the instruments are non-invasive, \emph{i.e.}, restricted to orthogonal, projective measurements. We then prove that there do not exist non-Markovian quantum processes that have finite Markov order with respect to all possible instruments; the same process exhibits distinct memory effects with respect to different probing instruments. This naturally leads to a relaxed definition of quantum Markov order with respect to specified sequences of instruments. The memory effects captured by different choices of instruments vary dramatically, providing a rich landscape for future exploration.

arXiv comment4.5+2 pages, 3 figures

References in corpus (46)

• Dynamical Decoupling of Open Quantum Systems
• Non-Markovian dynamics in open quantum systems
• Quantum correlations with no causal order
• Theoretical framework for quantum networks
• Memory in network flows and its effects on spreading dynamics and community detection
• Quantum Circuits Architecture
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Concepts of quantum non-Markovianity: a hierarchy
• Transforming quantum operations: quantum supermaps
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Operational Markov condition for quantum processes
• Quantum conditional mutual information and approximate Markov chains
• Quantum causal modelling
• Thermodynamical Control by Frequent Quantum Measurements
• Quantum common causes and quantum causal models
• Witnessing causal nonseparability
• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• Monotonicity of quantum relative entropy revisited
• Causal and causally separable processes
• Time-delayed quantum feedback control
• Master equations for correlated quantum channels
• Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise
• Composite quantum collision models
• On a quantitative method to analyse dynamical and measurement noise
• Exploiting Non-Markovianity of the Environment for Quantum Control
• On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise
• Robustness of quantum Markov chains
• Operational approach to open dynamics and quantifying initial correlations
• Multivariate Trace Inequalities
• An introduction to operational quantum dynamics
• Characterizing quantum dynamics with initial system-environment correlations
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Universal recovery map for approximate Markov chains
• Updating the Born rule
• Tomographically reconstructed master equations for any open quantum dynamics
• Open quantum systems with delayed coherent feedback
• Entanglement, non-Markovianity, and causal non-separability
• Positivity in the presence of initial system-environment correlation
• Preparation of states in open quantum mechanics
• Quantum non-Markovian piecewise dynamics from collision models
• Analysis of stochastic time series in the presence of strong measurement noise
• Quantum error correction with degenerate codes for correlated noise
• Markov properties in presence of measurement noise
• Probing the Non-Classicality of Temporal Correlations
• Removing correlations in signals transmitted over a quantum memory channel
• Measuring and Suppressing Error Correlations in Quantum Circuits

Cited by in corpus (56)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Demonstration of non-Markovian process characterisation and control on a quantum processor
• Completely Positive Divisibility Does Not Mean Markovianity
• Machine learning non-Markovian quantum dynamics
• Non-Markovian Quantum Process Tomography
• When is a non-Markovian quantum process classical?
• Quantum metrology for non-Markovian processes
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Tensor network based machine learning of non-Markovian quantum processes
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Randomized benchmarking for non-Markovian noise
• Fisher information of correlated stochastic processes
• Detection of quantum non-Markovianity close to the Born-Markov approximation
• Exponential improvement for quantum cooling through finite-memory effects
• Experimental Demonstration of Instrument-specific Quantum Memory Effects and Non-Markovian Process Recovery for Common-Cause Processes
• Markovianization with approximate unitary designs
• Non-Markovian Memory Strength Bounds Quantum Process Recoverability
• Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Quantum Uncertainty Principles for Measurements with Interventions
• Implementing quantum dimensionality reduction for non-Markovian stochastic simulation
• The Uncertainty Principle of Quantum Processes
• Equilibration of Multitime Quantum Processes in Finite Time Intervals
• Equilibration on average in quantum processes with finite temporal resolution
• Quantum Process Identification: A Method for Characterizing Non-Markovian Quantum Dynamics
• Memory Effects in Quantum Processes
• Non-Markovian memory in IBMQX4
• Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics
• Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
• Universal construction of decoders from encoding black boxes
• Detection of Bidirectional System-Environment Information Exchanges
• Perturbation theory for operational quantum non-Markovianity
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Hidden Quantum Memory: Is Memory There When Somebody Looks?
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system
• Quantum non-Markovian "casual bystander" environments
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Protecting collective qubits from non-Markovian dephasing
• Classical and quantum parts of conditional mutual information for open quantum systems
• Entropic witness for quantum memory in open system dynamics
• Process tensor distinguishability measures
• Optimality and Complexity in Measured Quantum-State Stochastic Processes
• Equilibration and Typicality in Quantum Processes
• Purely quantum memory in closed systems observed via imperfect measurements
• Violation of Diagonal Non-Invasiveness: A Hallmark of Non-Classical Memory Effects
• George Sudarshan and Quantum Dynamics
• Leggett-Garg inequalities for multitime processes
• Connecting Commutativity and Classicality for Multi-Time Quantum Processes
• Diagnosing chaos with projected ensembles of process tensors
• Geometric signature of non-Markovian dynamics
• Quantum-optical reset with classical memory
• Process Tensor Approaches to Non-Markovian Quantum Dynamics