Mixing Time of Open Quantum Systems via Hypocoercivity

• URL: http://arxiv.org/abs/2404.11503v1
• Date: Wed, 17 Apr 2024 15:58:17 GMT
• Title: Mixing Time of Open Quantum Systems via Hypocoercivity
• Abstract summary: Existing approaches for estimating the mixing time of open quantum systems often rely on the spectral gap estimation of the Lindbladian generator. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.
• Score: 5.327284412522592
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be challenging to obtain in practice. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately, thus circumventing the need for a priori estimation of the spectral gap of the full Lindbladian generator. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.

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