Self-restricting Noise and Exponential Relative Entropy Decay Under Unital Quantum Markov Semigroups

• URL: http://arxiv.org/abs/2203.03745v4
• Date: Thu, 01 May 2025 17:09:48 GMT
• Title: Self-restricting Noise and Exponential Relative Entropy Decay Under Unital Quantum Markov Semigroups
• Authors: Nicholas LaRacuente,
• Abstract summary: We analyze continuous processes that combine dissipative with Hamiltonian time-evolution.<n>We show that when dissipation is much stronger than Hamiltonian time-evolution, exponential decay toward the semigroup's decoherence-free subspace is bounded inversely in the decay rate of the dissipative part alone.
• Score: 0.8702432681310401
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: States of open quantum systems often decay continuously under environmental interactions. Quantum Markov semigroups model such processes in dissipative environments. It is known that finite-dimensional quantum Markov semigroups with GNS detailed balance universally obey complete modified logarithmic Sobolev inequalities (CMLSIs), yielding exponential decay of relative entropy to a subspace of fixed point states. We analyze continuous processes that combine dissipative with Hamiltonian time-evolution, precluding this notion of detailed balance. First, we find counterexamples to CMLSI-like decay for these processes and determine conditions under which it fails. In contrast, we prove that despite its absence at early times, exponential decay re-appears for unital, finite-dimensional quantum Markov semigroups at finite timescales. Finally, we show that when dissipation is much stronger than Hamiltonian time-evolution, the rate of eventual, exponential decay toward the semigroup's decoherence-free subspace is bounded inversely in the decay rate of the dissipative part alone. Dubbed self-restricting noise, this inverse relationship arises when strong damping suppresses effects that would otherwise spread noise beyond its initial subspace.

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