Generalising the Horodecki criterion to nonprojective qubit measurements

• URL: http://arxiv.org/abs/2109.09890v3
• Date: Fri, 7 Jan 2022 00:06:42 GMT
• Title: Generalising the Horodecki criterion to nonprojective qubit measurements
• Authors: Michael J. W. Hall and Shuming Cheng
• Abstract summary: Horodecki criterion requires suitable projective measurements on two qubit observables. We provide necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. We also show that for certain ranges of measurement strengths it is only possible to violate the Clauser-Horne-Shimony-Holt inequality via biased measurements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that suitable projective measurements can be made on each qubit, and is not sufficient for scenarios in which noisy or weak measurements are either desirable or unavoidable. By characterising two-valued qubit observables in terms of strength, bias, and directional parameters, we address such scenarios by providing necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. In particular, we find the achievable maximal values of the CHSH parameter for unbiased measurements on arbitrary states, and, alternatively, for arbitrary measurements on states with maximally-mixed marginals, and determine the optimal angles in some cases. We also show that for certain ranges of measurement strengths it is only possible to violate the CHSH inequality via biased measurements. Finally, we use the CHSH inequality to obtain a simple necessary condition for the compatibility of two qubit observables.

Related papers

• More nonlocality with less incompatibility in higher dimensions: Bell vs prepare-measure scenarios [1.224954637705144]
  We show that the violation of the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality responds non-monotonically with the amount of incompatibility. Unlike in the CHSH case, the maximally violating state in higher dimensions depends on the amount of measurement incompatibility.
  arXiv  Detail & Related papers  (2024-11-17T18:55:54Z)
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation [2.532202013576547]
  In a bipartite Bell scenario, the measurement incompatibility in one wing is both necessary and sufficient to reveal the nonlocality. We argue that it is the generalised contextuality that provides a restriction to the allowed degree of measurement incompatibility of any viable theory of nature.
  arXiv  Detail & Related papers  (2024-06-23T12:30:23Z)
• Resource-efficient high-dimensional entanglement detection via symmetric projections [0.0]
  We introduce two families of criteria for detecting and quantifying the entanglement of a bipartite quantum state of arbitrary local dimension. Both criteria give a qualitative result in terms of the state's entanglement dimension and a quantitative result in terms of its fidelity with the maximally entangled state.
  arXiv  Detail & Related papers  (2023-04-09T16:38:36Z)
• 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)
• The gap persistence theorem for quantum multiparameter estimation [14.334779130141452]
  We show that it is impossible to saturate the Holevo Cram'er-Rao bound (HCRB) for several physically motivated problems. We further prove that if the SLDCRB cannot be reached with a single copy of the probe state, it cannot be reached with collective measurements on any finite number of copies of the probe state.
  arXiv  Detail & Related papers  (2022-08-15T18:01:22Z)
• Mermin and Svetlichny inequalities for non-projective measurement observables [0.0]
  We find that for certain ranges of measurement strengths, it is possible to violate Mermin and Svetlichny inequalities only by biased measurement observables. The necessary and sufficient criteria of violating any one of the six possible Mermin and Svetlichny inequalities are also derived.
  arXiv  Detail & Related papers  (2022-03-14T13:47:15Z)
• 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)
• Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing [87.17253904965372]
  We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. We show that these errors decrease exponentially with decay rates given by the measured relative entropies between the two states.
  arXiv  Detail & Related papers  (2021-04-30T00:52:48Z)
• Discrimination of quantum states under locality constraints in the many-copy setting [18.79968161594709]
  We prove that the optimal average error probability always decays exponentially in the number of copies. We show an infinite separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB) On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB.
  arXiv  Detail & Related papers  (2020-11-25T23:26:33Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• 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)

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.