Geometric approach to quantum statistical inference

• URL: http://arxiv.org/abs/2008.09129v2
• Date: Mon, 31 Aug 2020 15:15:52 GMT
• Title: Geometric approach to quantum statistical inference
• Authors: Marcin Jarzyna and Jan Kolodynski
• Abstract summary: We study quantum statistical inference tasks of hypothesis testing and their canonical variations. We focus on the geometric approach to data inference problems, within which the aforementioned measures can be neatly interpreted. We discuss exemplary applications of such a geometric approach to problems of quantum parameter estimation, "speed limits" and thermodynamics.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial differences which arise in the quantum regime in contrast to the classical setting. In our analysis, we primarily focus on the geometric approach to data inference problems, within which the aforementioned measures can be neatly interpreted as particular forms of divergences that quantify distances in the space of probability distributions or, when dealing with quantum systems, of density matrices. Moreover, with help of the standard language of Riemannian geometry we identify both the metrics such divergences must induce and the relations such metrics must then naturally inherit. Finally, we discuss exemplary applications of such a geometric approach to problems of quantum parameter estimation, "speed limits" and thermodynamics.

Related papers

• Fluctuation-Dissipation Theorem and Information Geometry in Open Quantum Systems [2.203892199657599]
  We propose a fluctuation-dissipation theorem in open quantum systems from an information-theoretic perspective. We define the fidelity susceptibility that measures the sensitivity of the systems under perturbation and relate it to the fidelity correlator that characterizes the correlation behaviors for mixed quantum states.
  arXiv  Detail & Related papers  (2024-09-27T17:45:02Z)
• Dimension matters: precision and incompatibility in multi-parameter quantum estimation models [44.99833362998488]
  We study the role of probe dimension in determining the bounds of precision in quantum estimation problems. We also critically examine the performance of the so-called incompatibility (AI) in characterizing the difference between the Holevo-Cram'er-Rao bound and the Symmetric Logarithmic Derivative (SLD) one.
  arXiv  Detail & Related papers  (2024-03-11T18:59:56Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Numerical ranges and geometry in quantum information: Entanglement, uncertainty relations, phase transitions, and state interconversion [0.0]
  I show results relevant to numerical ranges -- the sets of simultaneously attainable expectation values of several observables. I apply this notion in the problems related to uncertainty relations, entanglement detection, and determining bounds for the value of spectral gap.
  arXiv  Detail & Related papers  (2023-03-13T18:14:40Z)
• Entanglement and Quantum Correlation Measures from a Minimum Distance Principle [0.0]
  Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science. We derive an explicit measure able to quantify the degree of quantum correlation for pure or mixed multipartite states. We prove that our entanglement measure is textitfaithful in the sense that it vanishes only on the set of separable states.
  arXiv  Detail & Related papers  (2022-05-14T22:18:48Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Information geometric approach to mixed state quantum estimation [0.28675177318965034]
  We will approach a problem of uniparametric statistical inference from an information-geometric perspective. We will obtain the generalised Bhattacharyya higher-order corrections for the Cram'er-Rao bound, where the statistics is given by a mixed quantum state.
  arXiv  Detail & Related papers  (2020-12-05T17:20:35Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Generalized Sliced Distances for Probability Distributions [47.543990188697734]
  We introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs) GSPMs are rooted in the generalized Radon transform and come with a unique geometric interpretation. We consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum.
  arXiv  Detail & Related papers  (2020-02-28T04:18:00Z)
• Uncertainty and Trade-offs in Quantum Multiparameter Estimation [0.0]
  Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. An uncertainty relation emerges between achievable variances of the different estimators.
  arXiv  Detail & Related papers  (2020-02-14T10:43:40Z)
• Direct estimation of quantum coherence by collective measurements [54.97898890263183]
  We introduce a collective measurement scheme for estimating the amount of coherence in quantum states. Our scheme outperforms other estimation methods based on tomography or adaptive measurements. We show that our method is accessible with today's technology by implementing it experimentally with photons.
  arXiv  Detail & Related papers  (2020-01-06T03:50:42Z)

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.