A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC

• URL: http://arxiv.org/abs/2312.07646v1
• Date: Tue, 12 Dec 2023 18:07:13 GMT
• Title: A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC
• Authors: Jonah Kudler-Flam, Samuel Leutheusser, Adel A. Rahman, Gautam Satishchandran, and Antony J. Speranza
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While von Neumann entropies for subregions in quantum field theory universally contain ultraviolet divergences, differences between von Neumann entropies are finite and well-defined in many physically relevant scenarios. We demonstrate that such a notion of entropy differences can be rigorously defined in quantum field theory in a general curved spacetime by introducing 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. This prescription reproduces formulas for entropy differences that coincide with heuristic formulas widely used in the literature, and we prove that it satisfies desirable properties such as unitary invariance and concavity. As an application, we provide proofs of the Bekenstein bound and the quantum null energy condition, formulated directly in terms of vacuum-subtracted von Neumann entropies.

Related papers

• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Entanglement entropy in conformal quantum mechanics [68.8204255655161]
  We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory.
  arXiv  Detail & Related papers  (2023-06-21T14:21:23Z)
• 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)
• Asymptotic Equipartition Theorems in von Neumann algebras [24.1712628013996]
  We show that the smooth max entropy of i.i.d. states on a von Neumann algebra has an rate given by the quantum relative entropy. Our AEP not only applies to states, but also to quantum channels with appropriate restrictions.
  arXiv  Detail & Related papers  (2022-12-30T13:42:35Z)
• Entropy of quantum states [0.0]
  We give a purely algebraic definition of entropy for states of an algebra of observables. The entropy so defined satisfies all the desirable thermodynamic properties, and reduces to the von Neumann entropy in the quantum mechanical case. It can be shown to be equal to the von Neumann entropy of the unique representative density matrix belonging to the operator algebra of a multiplicity-free Hilbert-space representation.
  arXiv  Detail & Related papers  (2021-04-26T14:23:55Z)
• 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)
• 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)
• Variational approach to relative entropies (with application to QFT) [0.0]
  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.
  arXiv  Detail & Related papers  (2020-09-10T17:41:28Z)
• Entropy and relative entropy from information-theoretic principles [24.74754293747645]
  We find that every relative entropy must lie between the R'enyi divergences of order $0$ and $infty$. Our main result is a one-to-one correspondence between entropies and relative entropies.
  arXiv  Detail & Related papers  (2020-06-19T14:50:44Z)
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy [0.0]
  We study odd entanglement entropy holographically dual to the entanglement wedge cross section. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy.
  arXiv  Detail & Related papers  (2020-04-08T18:00:01Z)

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.