Mappings preserving quantum Renyi's entropies in von Neumann algebras

• URL: http://arxiv.org/abs/2302.02282v1
• Date: Sun, 5 Feb 2023 02:41:39 GMT
• Title: Mappings preserving quantum Renyi's entropies in von Neumann algebras
• Authors: Andrzej {\L}uczak, Hanna Pods\k{e}dkowska, Rafa{\l} Wieczorek
• Abstract summary: A normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such a map does not change the entropy of any density if and only if it is a Jordan *-isomorphism on the algebra.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such a map does not change the entropy of any density if and only if it is a Jordan *-isomorphism on the algebra.

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)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling [22.20907440445493]
  We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) This formulation does not depend on the discretization of the Schr"odinger equation and recurrence relations of special functions. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator.
  arXiv  Detail & Related papers  (2023-04-04T03:02:03Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• 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)
• 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)
• 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)
• Trace- and improved data processing inequalities for von Neumann algebras [0.0]
  We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The natural applications of our results are in quantum field theory where the von Neumann algebras are known to be of type III.
  arXiv  Detail & Related papers  (2021-02-15T11:36:44Z)
• Multivariate Trace Inequalities, p-Fidelity, and Universal Recovery Beyond Tracial Settings [4.56877715768796]
  We show that the physics of quantum field theory and holography motivate entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki $L_p$ spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras.
  arXiv  Detail & Related papers  (2020-09-24T21:05:13Z)
• Quantum weak invariants: Dynamical evolution of fluctuations and correlations [0.0]
  Weak invariants are time-dependent observables with conserved expectation values. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital.
  arXiv  Detail & Related papers  (2020-09-16T22:18:58Z)

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.