Dynamical Characterization of Quantum Coherence

• URL: http://arxiv.org/abs/2407.11568v2
• Date: Mon, 12 Aug 2024 01:58:25 GMT
• Title: Dynamical Characterization of Quantum Coherence
• Authors: Hai Wang,
• Abstract summary: We show that for time-independent Hamiltonians, quantum coherence is the average evolution speed and vice versa. Our results definitely clarify the role coherence playing in quantum systems' dynamics, correlating quantum resources with quantum dynamics.
• Score: 2.7624036517702577
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum coherence, rooted in the superposition nature of quantum mechanics, is one core quantum resource in quantum technologies. Until now, various measures, operational interpretations and generalizations about coherence have been proposed. However, it is still not clear about the role coherence playing in quantum dynamics. In this work, in terms of unitary evolutions, the effect of coherence is fully exhibited. Firstly, by introducing the new concept, average quantum distance, we show that for time-independent Hamiltonians, quantum coherence is the average evolution speed and vice versa. Secondly, beyond this average setting, for general cases, we show that how coherence and Hamiltonians' eigenvalues determine the instantaneous evolution speed together, where their trade-off is actually the energy uncertainty. Our results definitely clarify the role coherence playing in quantum systems' dynamics, correlating quantum resources with quantum dynamics.

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