Optimal state pairs for non-Markovian quantum dynamics

Abstract

We study a recently proposed measure for the quantification of quantum non-Markovianity in the dynamics of open systems which is based on the exchange of information between the open system and its environment. This measure relates the degree of memory effects to certain optimal initial state pairs featuring a maximal flow of information from the environment back to the open system. We rigorously prove that the states of these optimal pairs must lie on the boundary of the space of physical states and that they must be orthogonal. This implies that quantum memory effects are maximal for states which are initially distinguishable with certainty, having a maximal information content. Moreover, we construct an explicit example which demonstrates that optimal quantum states need not be pure states.

6 pages, 2 figures

References in corpus (16)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Entanglement and non-Markovianity of quantum evolutions
• Assessing non-Markovian dynamics
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Measure for the Non-Markovianity of Quantum Processes
• Non-Markovian quantum jumps
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Non-Markovian quantum dynamics: local versus non-local
• Non-Markovianity assisted Steady State Entanglement
• Markovian and non-Markovian dynamics in quantum and classical systems
• Quantifying, characterizing and controlling information flow in ultracold atomic gases
• Measuring non-Markovianity of processes with controllable system-environment interaction
• Quantum Semi-Markov Processes
• Non-Markovianity, Loschmidt echo and criticality: a unified picture
• Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain

Cited by in corpus (96)

• Non-Markovian dynamics in open quantum systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Geometrical characterization of non-Markovianity
• Quantum speedup in a memory environment
• Comparative study of non-Markovianity measures in exactly solvable one and two qubit models
• Collision model for non-Markovian quantum dynamics
• Quantum regression theorem and non-Markovianity of quantum dynamics
• Generalized trace distance measure connecting quantum and classical non-Markovianity
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Implications of non-Markovian dynamics for the Landauer bound
• Harnessing non-Markovian quantum memory by environmental coupling
• An out-of-equilibrium non-Markovian Quantum Heat Engine
• Non-Markovian quantum dynamics: What does it mean?
• Non-unital non-Markovianity of quantum dynamics
• Non-Markovian master equations from piecewise dynamics
• Temperature effects on quantum non-Markovianity via collision models
• On the spectral origin of non-Markovianity: an exact finite model
• Employing Non-Markovian effects to improve the performance of a quantum Otto refrigerator
• Non-Markovianity-assisted high-fidelity Deutsch-Jozsa algorithm in diamond
• Two-qubit non-Markovianity induced by a common environment
• Accuracy of the quantum regression theorem for photon emission from a quantum dot
• Effects of the rotating wave and secular approximations on non-Markovianity
• There is no general connection between the quantum speed limit and non-Markovianity
• Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
• Non-Markovian dynamics of single- and two-qubit systems interacting with Gaussian and non-Gaussian fluctuating transverse environments
• Synchronization and Non-Markovianity in open quantum systems
• Revealing memory effects in phase-covariant quantum master equations
• Experimental emulation of quantum non-Markovian dynamics and coherence protection in the presence of information backflow
• Entropic bounds on information backflow
• Hierarchical environment-assisted dynamical speedup control
• Estimating the degree of non-Markovianity using machine learning
• Excited-state quantum phase transition and the quantum speed limit
• Information backflow as a resource for entanglement
• Competition between memory-keeping and memory-erasing decoherence channels
• Driving-induced amplification of non-Markovianity in open quantum systems evolution
• Entangling protocols due to non-Markovian dynamics
• Non-Markovian effects in the spin-boson model at zero temperature
• Entropic and trace distance based measures of non-Markovianity
• Heat flux and information backflow in cold condensed matter systems
• Quantum simulation of non-Markovianity using the quantum Zeno effect
• Bose-Hubbard lattice as a controllable environment for open quantum systems
• Non-Markovian qubit dynamics induced by Coulomb crystals
• Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems
• Non-Markovian qubit dynamics in a circuit-QED setup
• Quantum speedup, non-Markovianity and formation of bound state
• Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system
• Certifiability criterion for large-scale quantum systems
• Quantifying non-Markovianity via conditional mutual information
• Universal quantum uncertainty relations between non-ergodicity and loss of information
• Optomechanical second-order sidebands and group delays in a spinning resonator with parametric amplifier and non-Markovian effects
• Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility
• Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?
• Multiple single-photon generations in three-level atoms coupled to cavity with non-Markovian effects
• Impurity dephasing in a Bose-Hubbard model
• Quantum Models of Consciousness from a Quantum Information Science Perspective
• Discrete dynamics and non-Markovianity
• Memory in quantum processes with indefinite time direction and causal order
• Determining the squeezing in multimode fields using nonlocal quantum probes
• Noise induced Non-Markovianity
• Read-out of Quasi-periodic Systems using Qubits
• Memory effects in quantum dynamics modelled by quantum renewal processes
• Experimental Snapshot Verification of non-Markovianity with Unknown System-Probe Coupling
• Non-Markovianity is not a resource for quantum spatial search on a star graph subject to generalized percolation
• Non-Markovian effect on remote state preparation
• Non-Markovian Equilibration Controlled by Symmetry Breaking
• Detecting non-Markovianity from continuous monitoring
• Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
• Quantum non-Markovian behavior at the chaos border
• Complete positivity, positivity and long-time asymptotic behavior in a two-level open quantum system
• Non-markovianity and bound states in quantum walks with a phase impurity
• Non-Markovianity and memory of the initial state
• Minimalistic analytical approach to non-Markovian open quantum systems
• Non-Markovian dynamics of few emitters in a laser-driven cavity
• Interplay between Non-Markovianity of Noise and Dynamics in Quantum Systems
• Transient Dynamics and Homogenization in Incoherent Collision Models
• Information-Theoretic Meaning of Quantum Information Flow and Its Applications to Amplitude Amplification Algorithms
• Markovian and non-Markovian dynamics induced by a generic environment
• Bounds for the divisibility-based and distinguishability-based non-Markovianity measures
• Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories
• Quantum dynamical speedup for correlated initial states
• Nonequilibrium steady states in multi-bath quantum collision models
• Distillation of quantum non-Markovianity
• Dressed bound states and non-Markovian dynamics with a whispering-gallery-mode microcavity coupled to a two-level atom and a semi-infinite photonic waveguide
• Non-Markovianity in the Adapted Caldeira-Leggett model
• Violation of the thermodynamic uncertainty relation in quantum collisional models
• Phase space measures of information flow in open systems: A quantum and classical perspective of non-Markovianity
• Nonlocal quantum memory effects in a correlated multimode field
• Inducing nontrivial qubit coherence through a controlled dispersive environment
• Learning the non-Markovian features of subsystem dynamics
• Critical assessment of information back-flow in measurement-free teleportation
• Frontiers of open quantum system dynamics
• Non-Markovian steady states of a driven two-level system
• Ergotropy-Based Quantum Thermodynamics
• Open quantum dynamics with singularities: Master equations and degree of non-Markovianity
• Efficient Scheme of Experimental Quantifying non-Markovianity in High-Dimension Systems
• Control of memory effects in a spin-boson system by periodic driving