Quantum relative entropy for unravelings of master equations

• URL: http://arxiv.org/abs/2511.22976v1
• Date: Fri, 28 Nov 2025 08:31:14 GMT
• Title: Quantum relative entropy for unravelings of master equations
• Authors: Marcos Ruibal Ortigueira, Robert de Keijzer, Luke Visser, Oliver Tse, Servaas Kokkelmans,
• Abstract summary: This work explores connections between the quantum relative entropy of two faithful states $,$ and the Kullback-Leibler divergences of classical measures $,$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work explores connections between the quantum relative entropy of two faithful states $ρ,σ$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $μ,ν$. Here, $μ$ and $ν$ are measures on the space of pure states, realizing $ρ$ and $σ$ respectively. The motivation for this result is to establish a notion of quantum relative entropy in the space of pure state distributions, which are the resulting objects of unravelings of the Lindblad equation, such as the stochastic Schrödinger equation. Our results show that the measures that achieve the minimal KL divergence are those supported on a (possibly non-orthogonal) common basis between $ρ$ and $σ$. Using the classical and quantum data-processing inequalities, our notion of quantum relative entropy is shown to be equivalent to the Belavkin-Staszewski entropy on states, revealing new insights on this quantity. Furthermore, the common basis is used to provide a novel proof of contraction of the relative entropy under Lindblad flow and offers insights into results from large deviation theory.

Related papers

• Tight any-shot quantum decoupling [23.729027844524893]
  We prove a novel one-shot decoupling theorem formulated in terms of quantum entropy relative distance.<n>We show that this bound is ensemble-tight in quantum relative entropy distance.
  arXiv  Detail & Related papers  (2026-02-19T15:01:26Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• On Estimating the Quantum Tsallis Relative Entropy [10.925697720070426]
  The relative entropy between quantum states quantifies their distinguishability.<n>We show that for any constant $alpha in (0, 1)$, the $alpha$-Tsallis relative entropy between two quantum states of rank $r$ can be estimated.<n>We also show that the quantum state distinguishability problems with respect to the quantum $alpha$-Tsallis relative entropy and quantum Hellinger distance are $mathsfQSZK$-complete in a certain regime.
  arXiv  Detail & Related papers  (2025-10-01T10:38:59Z)
• Entropy Flow at the Quantum Limit [32.461516972240865]
  We show that the entropy entrained by heat flow is unbounded even though the entropy itself tends to zero.<n>The correct quantum formula predicts that the heat produced in quantum processes is vastly smaller than previously believed.
  arXiv  Detail & Related papers  (2025-08-31T00:46:33Z)
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario [17.30562902622871]
  We introduce a tripartite quantum-memory-assisted entropic uncertainty relation.<n>We extend the relation to encompass multiple measurements conducted within multipartite systems.
  arXiv  Detail & Related papers  (2025-01-06T09:09:34Z)
• Continuity of entropies via integral representations [16.044444452278064]
  We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. We obtain a number of results: (1) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, resolving a conjecture by Wilde in this special case; (2) a stronger version of the Fannes-Audenaert inequality on quantum entropy; and (3) better estimates on the quantum capacity of approximately degradable channels.
  arXiv  Detail & Related papers  (2024-08-27T17:44:52Z)
• Limiting flux in quantum thermodynamics [0.0]
  In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. We propose a new upper bound for such flux in terms of quantum relative entropy, applicable even far from equilibrium and in the strong coupling regime.
  arXiv  Detail & Related papers  (2023-11-22T17:17:23Z)
• Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels [17.153903773911036]
  We prove an entropic uncertainty relation for two quantum channels. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy.
  arXiv  Detail & Related papers  (2023-01-20T02:34:31Z)
• Integral formula for quantum relative entropy implies data processing inequality [0.0]
  We prove the monotonicity of quantum relative entropy under trace-preserving positive linear maps. For a simple application of such monotonicities, we consider any divergence' that is non-increasing under quantum measurements. An argument due to Hiai, Ohya, and Tsukada is used to show that the infimum of such a divergence' on pairs of quantum states with prescribed trace distance is the same as the corresponding infimum on pairs of binary classical states.
  arXiv  Detail & Related papers  (2022-08-25T16:32:02Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• Relative Entropy via Distribution of Observables [0.0]
  We obtain formulas for Petz-R'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. All of the results presented here are valid in both finite and infinite dimensions.
  arXiv  Detail & Related papers  (2022-03-03T19:06:36Z)
• Optimized quantum f-divergences [6.345523830122166]
  I introduce the optimized quantum f-divergence as a related generalization of quantum relative entropy. I prove that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality. One benefit of this approach is that there is now a single, unified approach for establishing the data processing inequality for the Petz--Renyi and sandwiched Renyi relative entropies.
  arXiv  Detail & Related papers  (2021-03-31T04:15:52Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.