Quantum Complementarity through Entropic Certainty Principles

• URL: http://arxiv.org/abs/2005.01760v1
• Date: Mon, 4 May 2020 18:02:47 GMT
• Title: Quantum Complementarity through Entropic Certainty Principles
• Authors: Javier M. Magan and Diego Pontello
• Abstract summary: Uncertainty relations arise by monotonicity of the relative entropies that participate in the underlying entropic certainty. In general, the entropic certainty principle naturally captures the physics of order/disorder parameters.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that the sum of two relative entropies, naturally related to the COA, is equal to the so-called algebraic index of the associated inclusion. Uncertainty relations then arise by monotonicity of the relative entropies that participate in the underlying entropic certainty. Examples and applications are described in quantum field theories with global symmetries, where the COA are formed by the charge-anticharge local operators (intertwiners) and the unitary representations of the symmetry group (twists), and in theories with local symmetries, where the COA are formed by Wilson and 't Hooft loops. In general, the entropic certainty principle naturally captures the physics of order/disorder parameters, a feature that makes it a generic handle for the information theoretic characterization of quantum phases.

Related papers

• Symmetry aspects in an ideal Bose gas at thermal equilibrium [0.0]
  It is possible to explain certain new fundamental symmetry aspects of ideal and very weakly interacting Bose gases. The propagation of one-directional time arises from the pre-defined and equivalent convergence of independent quantum fields. It is shown that Glauber's coherent states are related to the definition of the quantized field.
  arXiv  Detail & Related papers  (2024-10-12T08:55:34Z)
• 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)
• Entanglement monogamy via multivariate trace inequalities [12.814476856584346]
  We derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. We give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement.
  arXiv  Detail & Related papers  (2023-04-28T14:36:54Z)
• 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)
• 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)
• R\'enyi entropies and negative central charges in non-Hermitian quantum systems [0.0]
  We propose a natural extension of entanglement and R'enyi entropies to non-Hermitian quantum systems. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and R'enyi entropies.
  arXiv  Detail & Related papers  (2021-07-27T18:00:01Z)
• Quantum Fokker-Planck Dynamics [0.0]
  This paper aims to obtain a quantum counterpart of Fokker-Planck dynamics. Within this framework we present a quantization of the generalized Laplace operator. We then construct and examine the behaviour of the corresponding Markov semigroups.
  arXiv  Detail & Related papers  (2021-06-10T13:05:57Z)
• 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)
• Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and $c \rightarrow \infty $ Limit [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. The key feature of the formulation is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-09-12T23:48:52Z)
• 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)
• Generalized Entanglement, Charges and Intertwiners [0.0]
  We define a measure of entanglement entropy as a measure of information erased under restriction to a subspace of observables. We argue that the correct entanglement measure in the presence of charges is the sum of two terms; one measuring the entanglement of charge-neutral operators, and the other measuring the contribution of the bi-local intertwiners.
  arXiv  Detail & Related papers  (2020-05-22T20:49:05Z)

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.