Quantum Coherence, Dynamics and Their connections
- URL: http://arxiv.org/abs/2407.11568v1
- Date: Tue, 16 Jul 2024 10:21:59 GMT
- Title: Quantum Coherence, Dynamics and Their connections
- Authors: Hai Wang,
- Abstract summary: We show that for time-independent Hamiltonians, it is quantum coherence that determines the evolution speed on average.
For time-dependent Hamiltonians, we also give one upper bound for distance during one qubit's evolution.
For general quantum systems, the relation between quantum coherence and quantum dynamics is also discussed.
- 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 concept. Until now, the concept of coherence has also been generalized into projections and POVMs, and various coherence measures have been proposed. However, under the framework of quantum resource theory, interpretations of coherence and its various measures are usually grouped into the operational interpretation, where coherence measures correspond to the successful probability of discrimination tasks. Until now, it is still not clear which role quantum resources like coherence and entanglement play in states' evolutions and dynamical processes. In this work, by introducing the new concept, average quantum distance, we show that for time-independent Hamiltonians, it is quantum coherence that determines the evolution speed on average. Furthermore, for the single qubit system, we show that it is coherence that completely determines the system's evolution. Besides, for time-dependent Hamiltonians, we also give one upper bound for distance during one qubit's evolution. For general quantum systems, the relation between quantum coherence and quantum dynamics is also discussed. And as one byproduct, we examine the criterion for coherence measures about projections and propose one new condition called order preserving condition. One new coherence measure for projections is proposed. Compared with conditions for coherence about orthonormal basis, this new condition, order preserving, highlights the difference between orthogonal decompositions and orthonormal basis of Hilbert spaces and is satisfied by our new measure.
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