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  "path": "/papers/q-2026-03-04-2010/",
  "publishedAt": "2026-03-04T09:20:58.000Z",
  "site": "https://quantum-journal.org",
  "tags": [
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    "https://doi.org/10.22331/q-2026-03-04-2010"
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  "textContent": "Quantum 10, 2010 (2026).\n\nhttps://doi.org/10.22331/q-2026-03-04-2010\n\nStates 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.",
  "title": "Self-restricting Noise and Exponential Relative Entropy Decay Under Unital Quantum Markov Semigroups"
}