Operational Characterization of Divisibility of Dynamical Maps

Abstract

Divisibility of dynamical maps turns out to be a fundamental notion in characterising Markovianity of quantum evolution, although the decision problem for divisibility itself is computationally intractable. In this work, we propose the operational characterisation of divisibility of dynamical maps by exploiting distinguishability of quantum channels. We prove that distinguishability for any pair of quantum channels does not increase under divisible maps, and then, in terms of channel distinguishability with entanglement between system and $k$-dimensional ancillas, provide the operational characterization for the full hierarchy of the so-called $k$-divisiblity $(k=1,2,\dots )$. Finally, from the fact that min-entropy corresponds to the information-theoretic measure of distinguishability, the entropic characterisation to divisible maps is also provided.

6pages, 2 figures

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• Entanglement negativity as a universal non-Markovianity witness
• Maximally non-Markovian quantum dynamics without environment backflow of information
• How quantum evolution with memory is generated in a time-local way
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• The connection between time-local and time-nonlocal perturbation expansions
• Preserving quantum correlations and coherence with non-Markovianity
• Long-time Markovianity of multi-level systems in the rotating wave approximation
• Construction of propagators for divisible dynamical maps
• Effects of symmetry breaking of the structurally-disordered Hamiltonian ensembles on the anisotropic decoherence of qubits
• Information-Theoretic Meaning of Quantum Information Flow and Its Applications to Amplitude Amplification Algorithms
• Detecting Non-Markovianity via Quantified Coherence: Theory and Experiments
• Strongly non-quantitative classical information in quantum carriers
• Efficient and operational quantifier of non-divisibility in terms of channel discrimination