Resource theories of multi-time processes: A window into quantum non-Markovianity

Abstract

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess - corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.

arXiv comment35 pages, 8 figures, 3 tables

References in corpus (85)

• Quantum entanglement
• Dynamical Decoupling of Open Quantum Systems
• Quantum Resource Theories
• The role of quantum information in thermodynamics --- a topical review
• Fundamental limitations for quantum and nano thermodynamics
• Quantum Error Correction for Beginners
• Quantum correlations with no causal order
• Quantum Metrology in Non-Markovian Environments
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• On the Theory of Quantum Secret Sharing
• General Entanglement Breaking Channels
• Theoretical framework for quantum networks
• The Resource Theory of Stabilizer Computation
• Probabilistic theories with purification
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Quantum Circuits Architecture
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• Concepts of quantum non-Markovianity: a hierarchy
• Ancilla-assisted quantum process tomography
• Transforming quantum operations: quantum supermaps
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Quantum channels and memory effects
• A mathematical theory of resources
• Operational Markov condition for quantum processes
• Quantum causal modelling
• Quantum Channels with Memory
• Thermodynamical Control by Frequent Quantum Measurements
• Entanglement Theory and the Second Law of Thermodynamics
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Maximal Coherence and the Resource Theory of Purity
• Causal and causally separable processes
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Toward a general theory of quantum games
• Completely Positive Divisibility Does Not Mean Markovianity
• Comparison of Quantum Channels by Superchannels
• Operational Resource Theory of Quantum Channels
• Quantifying Operations with an Application to Coherence
• Approaches for approximate additivity of the Holevo information of quantum channels
• Thermodynamics of non-Markovian reservoirs and heat engines
• Machine learning non-Markovian quantum dynamics
• A resource theory of quantum memories and their faithful verification with minimal assumptions
• Exploiting Non-Markovianity of the Environment for Quantum Control
• Operational approach to open dynamics and quantifying initial correlations
• Robustness of Measurement, discrimination games and accessible information
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• A Resource Theory for Work and Heat
• An introduction to operational quantum dynamics
• Characterizing quantum dynamics with initial system-environment correlations
• Resource theory of asymmetric distinguishability for quantum channels
• Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories
• Quantum Markov Order
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• An operational approach to quantum stochastic thermodynamics
• The Operator Tensor Formulation of Quantum Theory
• Quantum violation of an instrumental test
• Classical quantum stochastic processes
• Superdensity Operators for Spacetime Quantum Mechanics
• Theoretical framework for Higher-Order Quantum Theory
• Updating the Born rule
• Computational Mechanics of Input-Output Processes: Structured transformations and the $\epsilon$-transducer
• Tomographically reconstructed master equations for any open quantum dynamics
• Fundamental work cost of quantum processes
• On a measure of distance for quantum strategies
• Fundamental limits on the capacities of bipartite quantum interactions
• Entanglement, non-Markovianity, and causal non-separability
• Almost Markovian processes from closed dynamics
• Reconstructing open quantum system dynamics with limited control
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Causal Boxes: Quantum Information-Processing Systems Closed under Composition
• The first law of general quantum resource theories
• A Unifying Framework for Spatial and Temporal Quantum Correlations
• Using quantum theory to reduce the complexity of input-output processes
• Quantification of quantum dynamics with input-output games
• Causation does not explain contextuality
• Information backflow as a resource for entanglement
• Non-Markovian quantum control as coherent stochastic trajectories
• Stochastic thermodynamics with arbitrary interventions
• Quantum Process Capability
• Thermodynamic utility of Non-Markovianity from the perspective of resource interconversion
• Quantifying Quantum-Mechanical Processes
• Equilibration on average in quantum processes with finite temporal resolution
• Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach
• Non-Markovianity of photon dynamics in a birefringent crystal

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• Operational Interpretation of the Choi Rank Through k-State Exclusion
• Capturing long-range memory structures with tree-geometry process tensors
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• One-shot manipulation of coherence in dynamic quantum resource theory
• Entropic witness for quantum memory in open system dynamics
• Entanglement-breaking channels are a quantum memory resource
• Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Process tensor distinguishability measures
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• Verifying Quantum Memory in the Dynamics of Spin Boson Models
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• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
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