Relative entropic uncertainty relation

• URL: http://arxiv.org/abs/2012.10080v2
• Date: Fri, 4 Jun 2021 15:01:22 GMT
• Title: Relative entropic uncertainty relation
• Authors: Stefan Floerchinger and Tobias Haas and Ben Hoeber
• Abstract summary: We find that a sum of relative entropies is bounded from above in a nontrivial way. This type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra. We find that a sum of relative entropies is bounded from above in a nontrivial way, which we illustrate with some examples.

Related papers

• 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)
• Non-Abelian symmetry can increase entanglement entropy [62.997667081978825]
  We quantify the effects of charges' noncommutation on Page curves. We show analytically and numerically that the noncommuting-charge case has more entanglement.
  arXiv  Detail & Related papers  (2022-09-28T18:00:00Z)
• Uncertainty relations from graph theory [0.0]
  Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. We derive uncertainty relations valid for any set of dichotomic observables. As applications, our results can be straightforwardly used to formulate entropic uncertainty relations, separability criteria and entanglement witnesses.
  arXiv  Detail & Related papers  (2022-07-05T17:57:31Z)
• 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)
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts [0.0]
  In a $d$ dimensional system and two mutually unbiased measurements, the sum of two information entropies is lower bounded by $ln d$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain. Here we consider the whole family of R'enyi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.
  arXiv  Detail & Related papers  (2021-07-26T18:48:26Z)
• Relative entropic uncertainty relation for scalar quantum fields [0.0]
  We introduce the notion of a functional relative entropy and show that it has a meaningful field theory limit. We show that the relation implies the multidimensional Heisenberg uncertainty relation.
  arXiv  Detail & Related papers  (2021-07-16T11:15:07Z)
• 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)
• Wehrl entropy, entropic uncertainty relations and entanglement [0.0]
  We show that the Wehrl-Lieb inequality is closer to equality than the usual Bialynicki-Birula and Mycielski entropic uncertainty relation almost everywhere. We show how a Wehrl mutual information can be used to obtain a measurable perfect witness for pure state bipartite entanglement.
  arXiv  Detail & Related papers  (2021-03-12T12:12:55Z)
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements [0.0]
  We obtain tripartite quantum memory-assisted entropic uncertainty relations. We show that the lower bounds of these relations have three terms that depend on the complementarity of the observables.
  arXiv  Detail & Related papers  (2021-03-11T21:35:04Z)
• 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)
• On the Estimation of Information Measures of Continuous Distributions [25.395010130602287]
  estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. We provide confidence bounds for simple histogram based estimation of differential entropy from a fixed number of samples. Our focus is on differential entropy, but we provide examples that show that similar results hold for mutual information and relative entropy as well.
  arXiv  Detail & Related papers  (2020-02-07T15:36:10Z)

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.