Variational approach to relative entropies (with application to QFT)

• URL: http://arxiv.org/abs/2009.05024v3
• Date: Tue, 13 Oct 2020 13:00:18 GMT
• Title: Variational approach to relative entropies (with application to QFT)
• Authors: Stefan Hollands
• Abstract summary: We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an "orbifolded" -- in the sense of conditional expectation -- system in terms of the Jones index. We take the opportunity to point out entropic certainty relation for arbitrary von Neumann subalgebras of a factor related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

Related papers

• A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC [0.0]
  We show that a notion of entropy differences can be rigorously defined in quantum field theory in a general curved spacetime. We introduce a novel, covariant regulator for the entropy based on the modular crossed product. This regulator associates a type II von Neumann algebra to each spacetime subregion, resulting in well-defined renormalized entropies.
  arXiv  Detail & Related papers  (2023-12-12T18:07:13Z)
• Towards Entanglement Entropy of Random Large-N Theories [0.0]
  We use the replica approach and the notion of shifted Matsubara frequency to compute von Neumann and R'enyi entanglement entropies. We demonstrate the flexibility of the method by applying it to examples of a two-site problem in presence of decoherence.
  arXiv  Detail & Related papers  (2023-03-03T18:21:54Z)
• Sandwiched Renyi Relative Entropy in AdS/CFT [0.0]
  We explore the role of sandwiched Renyi relative entropy in AdS/CFT and in finite-dimensional models of holographic quantum error correction. In particular, we discuss a suitable generalization of sandwiched Renyi relative entropy over finite-dimensional von Neumann algebras.
  arXiv  Detail & Related papers  (2022-04-16T01:13:29Z)
• On the Kullback-Leibler divergence between pairwise isotropic Gaussian-Markov random fields [93.35534658875731]
  We derive expressions for the Kullback-Leibler divergence between two pairwise isotropic Gaussian-Markov random fields. The proposed equation allows the development of novel similarity measures in image processing and machine learning applications.
  arXiv  Detail & Related papers  (2022-03-24T16:37:24Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling [77.34726150561087]
  We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths. Our approach is based on the exact time-local quantum master equation for the reduced open system states.
  arXiv  Detail & Related papers  (2021-09-24T11:19:22Z)
• R\'enyi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations [91.3755431537592]
  We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence. We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
  arXiv  Detail & Related papers  (2021-06-19T04:06:23Z)
• 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)
• Long-distance entanglement of purification and reflected entropy in conformal field theory [58.84597116744021]
  We study entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy. We find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour.
  arXiv  Detail & Related papers  (2021-01-29T19:00:03Z)
• Exact variance of von Neumann entanglement entropy over the Bures-Hall measure [3.8265321702445267]
  We study the statistical behavior of quantum entanglement over the Bures-Hall ensemble. Average von Neumann entropy over such an ensemble has been recently obtained.
  arXiv  Detail & Related papers  (2020-06-24T14:04:05Z)
• Approximate tensorization of the relative entropy for noncommuting conditional expectations [3.4376560669160385]
  We derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto finite-dimensional von Neumann algebras. We show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.
  arXiv  Detail & Related papers  (2020-01-22T12:20:53Z)

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.