Optimizing incompatible triple quantum measurements

• URL: http://arxiv.org/abs/2205.14561v1
• Date: Sun, 29 May 2022 02:40:13 GMT
• Title: Optimizing incompatible triple quantum measurements
• Authors: Hui-Hui Qin and Shao-Ming Fei
• Abstract summary: We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability inequality. The results give rise to plausible experimental verifications of such statistical distance based uncertainty relations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical Review A 99, 312107 (2019)], we give the analytical expressions of the optimal jointly measurable approximation to two kinds of triple incompatible unbiased qubit measurements. We also obtain the corresponding states which give the minimal approximation errors in measuring process. The results give rise to plausible experimental verifications of such statistical distance based uncertainty relations.

Related papers

• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Measurement uncertainty relation for three observables [3.021369108296711]
  We establish a measurement uncertainty relation (MUR) for three unbiased qubit observables. We derive a necessary and sufficient condition for the triplet MUR to be saturated and the corresponding optimal measurement.
  arXiv  Detail & Related papers  (2022-11-17T07:38:51Z)
• Testing Heisenberg's measurement uncertainty relation of three observables [3.021369108296711]
  Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for quantum foundations and quantum information science. We report the first experimental test of MURs for three quantum observables.
  arXiv  Detail & Related papers  (2022-11-17T07:38:31Z)
• Monotonicity and Double Descent in Uncertainty Estimation with Gaussian Processes [52.92110730286403]
  It is commonly believed that the marginal likelihood should be reminiscent of cross-validation metrics and that both should deteriorate with larger input dimensions. We prove that by tuning hyper parameters, the performance, as measured by the marginal likelihood, improves monotonically with the input dimension. We also prove that cross-validation metrics exhibit qualitatively different behavior that is characteristic of double descent.
  arXiv  Detail & Related papers  (2022-10-14T08:09:33Z)
• 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)
• Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency [59.48096489854697]
  The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We prove non-asymptotic upper bounds on the mean-squared error of such procedures. We establish its instance-dependent optimality in finite samples via matching non-asymptotic local minimax lower bounds.
  arXiv  Detail & Related papers  (2022-09-26T23:50:55Z)
• Experimentally determining the incompatibility of two qubit measurements [55.41644538483948]
  We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom.
  arXiv  Detail & Related papers  (2021-12-15T19:01:44Z)
• Optimized entropic uncertainty relations for multiple measurements [4.8723490038152635]
  We improve the lower bound of the entropic uncertainty relation for multiple measurements, termed as simply constructed bound (SCB) We verify that the SCB is tighter than Liu et al.'s result for arbitrary mutually unbiased basis measurements. It is believed that our findings would shed light on entropy-based uncertainty relations in the multiple measurement scenario.
  arXiv  Detail & Related papers  (2021-12-02T01:29:15Z)
• 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)
• The Aleatoric Uncertainty Estimation Using a Separate Formulation with Virtual Residuals [51.71066839337174]
  Existing methods can quantify the error in the target estimation, but they tend to underestimate it. We propose a new separable formulation for the estimation of a signal and of its uncertainty, avoiding the effect of overfitting. We demonstrate that the proposed method outperforms a state-of-the-art technique for signal and uncertainty estimation.
  arXiv  Detail & Related papers  (2020-11-03T12:11:27Z)
• Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Three-Outcome Qubit Measurements [1.4680035572775534]
  Information-theoretic uncertainty relations formulate the joint immeasurability of two non-commuting observables. Recent theoretical analysis predicts that projective measurements are not optimal. We experimentally test a tight information-theoretic measurement uncertainty relation for three-outcome positive-operator valued measures.
  arXiv  Detail & Related papers  (2020-05-27T15:09:25Z)

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.