Error estimation of different schemes to measure spin-squeezing inequalities

• URL: http://arxiv.org/abs/2311.17845v2
• Date: Thu, 22 Aug 2024 15:31:06 GMT
• Title: Error estimation of different schemes to measure spin-squeezing inequalities
• Authors: Jan Lennart Bönsel, Satoya Imai, Ye-Chao Liu, Otfried Gühne,
• Abstract summary: We show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations. We discuss how error bounds can be derived for nonlinear estimators with the help of their variances. Our methods can also be applied to spin-squeezing inequalities for qudits or for the statistical treatment of other nonlinear parameters of quantum states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: How can we analyze quantum correlations in large and noisy systems without quantum state tomography? An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations and variances. This allows detection of metrologically useful entanglement, but efficient strategies for estimating such nonlinear quantities have yet to be determined. In this paper we show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations, either involving all pair correlations or randomly chosen pair correlations. Then we analyze the estimation errors of our approaches in terms of a hypothesis test. For this purpose, we discuss how error bounds can be derived for nonlinear estimators with the help of their variances, characterizing the probability of falsely detecting a separable state as entangled. We focus on the spin-squeezing inequalities in multiqubit systems. Our methods, however, can also be applied to spin-squeezing inequalities for qudits or for the statistical treatment of other nonlinear parameters of quantum states.

Related papers

• Reference-frame-independent quantum metrology [0.0]
  We present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. We derive the metrological precision using an error propagation formula based solely on local unitary invariants. We analyze our results in the context of local decoherence and discuss its influences on the observed scaling.
  arXiv  Detail & Related papers  (2024-10-14T13:59:08Z)
• Interferometry of quantum correlation functions to access quasiprobability distribution of work [0.0]
  We use an interferometric scheme aided by an auxiliary system to reconstruct the Kirkwood-Dirac quasiprobability distribution. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics.
  arXiv  Detail & Related papers  (2024-05-31T17:32:02Z)
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state [0.0]
  We analytically study the scaling of quantum correlation measures on a one-dimensional containing a noninteracting impurity. We derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system.
  arXiv  Detail & Related papers  (2023-10-25T18:00:48Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• Statistical Efficiency of Score Matching: The View from Isoperimetry [96.65637602827942]
  We show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated. We formalize these results both in the sample regime and in the finite regime.
  arXiv  Detail & Related papers  (2022-10-03T06:09:01Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations [0.0]
  Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables will be limited by quantum mechanical uncertainty relations.
  arXiv  Detail & Related papers  (2021-06-02T09:58:38Z)
• Inequalities for complementarity in observed statistics [0.0]
  We show that, if the measured statistics does notfulfill the inequalities it is equivalent to the lack of a joint distribution for theincompatible observables. This is illustrated by path-interference duality ina Young interferometer.
  arXiv  Detail & Related papers  (2021-03-04T15:26:01Z)
• Nonlinear Independent Component Analysis for Continuous-Time Signals [85.59763606620938]
  We study the classical problem of recovering a multidimensional source process from observations of mixtures of this process. We show that this recovery is possible for many popular models of processes (up to order and monotone scaling of their coordinates) if the mixture is given by a sufficiently differentiable, invertible function.
  arXiv  Detail & Related papers  (2021-02-04T20:28:44Z)
• Interpolation and Learning with Scale Dependent Kernels [91.41836461193488]
  We study the learning properties of nonparametric ridge-less least squares. We consider the common case of estimators defined by scale dependent kernels.
  arXiv  Detail & Related papers  (2020-06-17T16:43:37Z)

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.