Enhanced Schmidt number criteria based on correlation trace norms

• URL: http://arxiv.org/abs/2402.09972v1
• Date: Thu, 15 Feb 2024 14:28:57 GMT
• Title: Enhanced Schmidt number criteria based on correlation trace norms
• Authors: Armin Tavakoli, Simon Morelli
• Abstract summary: The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of correlations obtained from seminal families of quantum measurements, specifically symmetric informationally complete measurements and mutually unbiased bases. Our criteria are strictly stronger than both the well-known fidelity witness criterion and the computable cross-norms or realignment criterion.

Related papers

• Re-examining Double Descent and Scaling Laws under Norm-based Capacity via Deterministic Equivalence [20.88908358215574]
  We investigate double descent and scaling laws in terms of weights rather than the number of parameters. Our results rigorously answer whether double descent exists under norm-based capacity and reshape the corresponding scaling laws.
  arXiv  Detail & Related papers  (2025-02-03T18:10:40Z)
• Schmidt number criterion via general symmetric informationally complete measurements [4.302984266310778]
  We derive a Schmidt number criterion based on the trace norm of the correlation matrix obtained from the general symmetric informationally complete measurements. We show that this Schmidt number criterion is more effective and superior than other criteria such as fidelity, CCNR, MUB, and EAM.
  arXiv  Detail & Related papers  (2024-12-13T12:01:37Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Absolute dimensionality of quantum ensembles [41.94295877935867]
  The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e.basis-independent, notion of dimensionality for ensembles of quantum states.
  arXiv  Detail & Related papers  (2024-09-03T09:54:15Z)
• Classification of joint quantum measurements based on entanglement cost of localization [42.72938925647165]
  We propose a systematic classification of joint measurements based on entanglement cost. We show how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.
  arXiv  Detail & Related papers  (2024-08-01T18:00:01Z)
• 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)
• Families of Schmidt-number witnesses for high dimensional quantum states [0.9790236766474201]
  Schmidt number is a quantity on the dimension entanglement of a bipartite state. We show the distance between a bipartite state and the set of states with Schmidt number less than k.
  arXiv  Detail & Related papers  (2024-03-01T03:25:53Z)
• Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds [0.0]
  An important and geometrically intuitive measure of translational asymmetry of a state is given by the trace-norm asymmetry. We show that the trace-norm asymmetry is equal to the average absolute imaginary part of the weak value of the generator of the translation group optimized over all possible orthonormal bases of the Hilbert space. We then use the link between the trace-norm asymmetry and the nonreal weak value to derive the relation between the trace-norm asymmetry with other basic concepts in quantum statistics.
  arXiv  Detail & Related papers  (2023-09-17T05:12:13Z)
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States [15.208790082352351]
  distillable randomness of a bipartite quantum state is an information-theoretic quantity. We prove measures of classical correlations and prove a number of their properties. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming.
  arXiv  Detail & Related papers  (2022-12-18T12:06:25Z)
• Probing the geometry of correlation matrices with randomized measurements [0.0]
  The generalized Bloch decomposition of a bipartite quantum state gives rise to a correlation matrix whose singular values provide rich information about non-local properties of the state. We provide a deeper insight into the geometry of the singular values of the correlation matrices of limited Schmidt number.
  arXiv  Detail & Related papers  (2022-11-17T15:59:59Z)
• Quantitative characterization of several entanglement detection criteria [0.0]
  We show that reduction, majorization, and the R'enyi-entropy-based criteria are very ineffective compared to the positive partial transpose. In the case of the R'enyi-entropy-based criterion, we show that the ratio of detectable entanglement increases with the order of the R'enyi entropy.
  arXiv  Detail & Related papers  (2022-07-05T13:48:23Z)
• Entanglement swapping and quantum correlations via Elegant Joint Measurements [5.252277280918264]
  We use hyper-entanglement to experimentally realize deterministic entanglement swapping based on quantum Elegant Joint Measurements. We report measurement fidelities no smaller than $97.4%$.
  arXiv  Detail & Related papers  (2022-03-30T11:09:20Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• 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)
• Nonlinear steering criteria for arbitrary two-qubit quantum systems [16.20946947543463]
  We present some nonlinear steering criteria applicable for arbitrary two-qubit quantum systems and optimized ones for symmetric quantum states. Compared with the existing linear steering criterion and entropic criterion, ours can certify more steerable states without selecting measurement settings or correlation weights.
  arXiv  Detail & Related papers  (2020-09-30T19:57:37Z)

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.