On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank

• URL: http://arxiv.org/abs/1906.06185v2
• Date: Wed, 22 Jan 2025 14:59:44 GMT
• Title: On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank
• Authors: Luigi Seveso, Francesco Albarelli, Marco G. Genoni, Matteo G. A. Paris,
• Abstract summary: We address the discontinuities of the quantum Fisher information (QFI) that may arise when the parameter of interest takes values that change the rank of the quantum statistical model. We revisit the classical and the quantum Cram'er-Rao theorems, show that they do not hold in these limiting cases, and discuss how this impacts on the relationship between the QFI and the Bures metric.
• Score: 0.0
• License:
• Abstract: We address the discontinuities of the quantum Fisher information (QFI) that may arise when the parameter of interest takes values that change the rank of the quantum statistical model. We revisit the classical and the quantum Cram\'er-Rao theorems, show that they do not hold in these limiting cases, and discuss how this impacts on the relationship between the QFI and the Bures metric. In order to illustrate the metrological implications of our findings, we present two paradigmatic examples, where we discuss in detail the role of the discontinuities and show that the Cram\'er-Rao may be easily violated.

Related papers

• Quantum criticality at the boundary of the non-Hermitian regime of a Floquet system [4.144331441157407]
  We investigate the dynamics of quantum scrambling in a non-Hermitian quantum kicked rotor. The rates of the linear growth are found to diverge to infinity, indicating the existence of quantum criticality at the boundary of the non-Hermitian regime.
  arXiv  Detail & Related papers  (2023-07-02T03:20:56Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models [62.997667081978825]
  In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work.
  arXiv  Detail & Related papers  (2023-02-27T13:42:40Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators [0.0]
  We consider the realistic situation in which the parameters of interest are the loss rate and the nonlinear coupling, whereas the amplitude of the coherent driving is known and tunable. We also investigate the performance of quadrature detection, and show that for both parameters the Fisher information oscillates in time, repeatedly approaching the corresponding QFI.
  arXiv  Detail & Related papers  (2022-12-09T20:50:33Z)
• Quantum Cram\'er-Rao bound for quantum statistical models with parameter-dependent rank [0.0]
  We argue that the limiting version of quantum Cram'er-Rao bound still holds when the parametric density operator changes its rank. We analyze a typical example of the quantum statistical models with parameter-dependent rank.
  arXiv  Detail & Related papers  (2021-11-01T13:23:04Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Taming singularities of the quantum Fisher information [0.0]
  singular QFIMs occur when the curvature of the metric vanishes in one or more directions. QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios.
  arXiv  Detail & Related papers  (2021-08-12T21:38:29Z)
• Quantum enhanced metrology of Hamiltonian parameters beyond the Cram\`er-Rao bound [0.0]
  This tutorial focuses on developments in quantum parameter estimation beyond the Cramer-Rao bound. It shows that an achievable bound to precision (beyond the Cramer-Rao) may be obtained in a closed form for the class of so-called controlled energy measurements.
  arXiv  Detail & Related papers  (2020-03-05T08:35:40Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)

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.