Exact variance of von Neumann entanglement entropy over the Bures-Hall measure

• URL: http://arxiv.org/abs/2006.13746v1
• Date: Wed, 24 Jun 2020 14:04:05 GMT
• Title: Exact variance of von Neumann entanglement entropy over the Bures-Hall measure
• Authors: Lu Wei
• Abstract summary: 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.
• Score: 3.8265321702445267
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Bures-Hall distance metric between quantum states is a unique measure that satisfies various useful properties for quantum information processing. In this work, we study the statistical behavior of quantum entanglement over the Bures-Hall ensemble as measured by von Neumann entropy. The average von Neumann entropy over such an ensemble has been recently obtained, whereas the main result of this work is an explicit expression of the corresponding variance that specifies the fluctuation around its average. The starting point of the calculations is the connection between correlation functions of the Bures-Hall ensemble and these of the Cauchy-Laguerre ensemble. The derived variance formula, together with the known mean formula, leads to a simple but accurate Gaussian approximation to the distribution of von Neumann entropy of finite-size systems. This Gaussian approximation is also conjectured to be the limiting distribution for large dimensional systems.

Related papers

• Closed-form solutions for the Salpeter equation [41.94295877935867]
  We study the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent problem, namely the B"aumer equation. This B"aumera corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy for small times and Gaussian diffusion for large times.
  arXiv  Detail & Related papers  (2024-06-26T15:52:39Z)
• Sampling and estimation on manifolds using the Langevin diffusion [45.57801520690309]
  Two estimators of linear functionals of $mu_phi $ based on the discretized Markov process are considered. Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion.
  arXiv  Detail & Related papers  (2023-12-22T18:01:11Z)
• Page curves and typical entanglement in linear optics [0.0]
  We study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We prove various results on the typicality of entanglement as measured by the R'enyi-2 entropy. Our main make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries.
  arXiv  Detail & Related papers  (2022-09-14T18:00:03Z)
• 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)
• 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)
• Second-order statistics of fermionic Gaussian states [3.8265321702445267]
  We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states. The focus is on the variance of von Neumann entropy and the mean entanglement capacity.
  arXiv  Detail & Related papers  (2021-11-16T04:18:25Z)
• 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)
• Entropy Production and the Role of Correlations in Quantum Brownian Motion [77.34726150561087]
  We perform a study on quantum entropy production, different kinds of correlations, and their interplay in the driven Caldeira-Leggett model of quantum Brownian motion.
  arXiv  Detail & Related papers  (2021-08-05T13:11:05Z)
• Kurtosis of von Neumann entanglement entropy [2.88199186901941]
  We study the statistical behavior of entanglement in quantum bipartite systems under the Hilbert-Schmidt ensemble. The main contribution of the present work is the exact formula of the corresponding fourth cumulant that controls the tail behavior of the distribution.
  arXiv  Detail & Related papers  (2021-07-21T22:20:10Z)
• 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)
• Fast approximations in the homogeneous Ising model for use in scene analysis [61.0951285821105]
  We provide accurate approximations that make it possible to numerically calculate quantities needed in inference. We show that our approximation formulae are scalable and unfazed by the size of the Markov Random Field. The practical import of our approximation formulae is illustrated in performing Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment, and also in likelihood ratio testing for anisotropy in the spatial patterns of yearly increases in pistachio tree yields.
  arXiv  Detail & Related papers  (2017-12-06T14:24:34Z)

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.