Revealing memory effects in phase-covariant quantum master equations

Abstract

We study and compare the sensitivity of multiple non-Markovianity indicators for a qubit subjected to general phase-covariant noise. For each of the indicators, we derive analytical conditions to detect the dynamics as non-Markovian. We present these conditions as relations between the time-dependent decay rates for the general open system dynamics and its commutative and unital subclasses. These relations tell directly if the dynamics is non-Markovian w.r.t.~each indicator, without the need to explicitly derive and specify the analytic form of the time-dependent coefficients. Moreover, with a shift in perspective, we show that if one assumes only the general form of the master equation, measuring the non-Markovianity indicators gives us directly non-trivial information on the relations between the unknown decay rates.

arXiv comment21 pages, 1 figure

References in corpus (31)

• Quantifying Coherence
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Non-Markovian dynamics in open quantum systems
• The Role of Relative Entropy in Quantum Information Theory
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Open Quantum Systems. An Introduction
• Universal state inversion and concurrence in arbitrary dimensions
• Distance measures to compare real and ideal quantum processes
• 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
• Canonical form of master equations and characterization of non-Markovianity
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• Geometrical characterization of non-Markovianity
• Optimal state pairs for non-Markovian quantum dynamics
• The ultimate precision limits for noisy frequency estimation
• Measuring non-Markovianity of processes with controllable system-environment interaction
• Quantifying non-Markovianity of continuous variable Gaussian dynamical maps
• Non-Markovianity, Loschmidt echo and criticality: a unified picture
• Experimental observation of weak non-Markovianity
• Coherence trapping and information back-flow in dephasing qubits
• Monotonicity of the Quantum Relative Entropy Under Positive Maps
• Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate
• Thermodynamic meaning and power of non-Markovianity
• Fundamental limits to frequency estimation: A comprehensive microscopic perspective
• Detecting non-Markovianity of quantum evolution via spectra of dynamical maps
• Role of non-Markovianity and backflow of information in the speed of quantum evolution
• High Resolution non-Markovianity in NMR
• Nonlocal memory assisted entanglement distribution in optical fibers
• Momentum-Resolved and Correlations Spectroscopy Using Quantum Probes
• The problem of coherent control in non-Markovian open quantum systems

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• Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
• Non-monotonic population and coherence evolution in Markovian open-system dynamics
• Quantifying information flow in quantum processes
• Divisibility of dynamical maps: Schrödinger vs. Heisenberg picture
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket
• Quantum speed limit and nonclassicality in open quantum system models using the Wigner function
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