Quantifying Non-Markovianity in Open Quantum Dynamics

Abstract

Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.

10 pages, 3 figures

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Surface codes: Towards practical large-scale quantum computation
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Strong quantum computational advantage using a superconducting quantum processor
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Efficient quantum state tomography
• Assessing non-Markovian dynamics
• Hybrid quantum-classical algorithms and quantum error mitigation
• Operational Markov condition for quantum processes
• Operator Space Entanglement Entropy in XY Spin Chains
• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
• An introduction to operational quantum dynamics
• Quantum Decoherence of Two Qubits
• Randomized benchmarking for non-Markovian noise
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States

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• Operational Markovianization in Randomized Benchmarking
• Randomised benchmarking for characterizing and forecasting correlated processes
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Quantifying Decoherence