Estimating coherence with respect to general quantum measurements

• URL: http://arxiv.org/abs/2109.14323v1
• Date: Wed, 29 Sep 2021 10:19:23 GMT
• Title: Estimating coherence with respect to general quantum measurements
• Authors: Jianwei Xu, Lin Zhang, Shao-Ming Fei
• Abstract summary: Generalized quantum coherence with respect to general positive operator-valued measurements (POVMs) has been presented. Several well-defined coherence measures, such as the relative entropy of coherence $C_r$, the $l_1$ norm of coherence $C_l_1$ and the coherence $C_T,alpha $ have been obtained.
• Score: 4.707579791895607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., to a von Neumann measurement. Recently, generalized quantum coherence with respect to general positive operator-valued measurements (POVMs) has been presented. Several well-defined coherence measures, such as the relative entropy of coherence $C_{r}$, the $l_{1}$ norm of coherence $C_{l_{1}}$ and the coherence $C_{T,\alpha }$ based on Tsallis relative entropy with respect to general POVMs have been obtained. In this work, we investigate the properties of $C_{r}$, $l_{1}$ and $C_{T,\alpha }$. We estimate the upper bounds of $C_{l_{1}}$; we show that the minimal error probability of the least square measurement state discrimination is given by $C_{T,1/2}$; we derive the uncertainty relations given by $C_{r}$, and calculate the average values of $C_{r}$, $C_{T,\alpha }$ and $C_{l_{1}}$ over random pure quantum states. All these results include the corresponding results of the conventional coherence as special cases.

Related papers

• Optimal convergence rates in trace distance and relative entropy for the quantum central limit theorem [2.7855886538423182]
  We show that for a centered $m$-mode quantum state with finite third-order moments, the trace distance between $rhoboxplus n$ and $rho_G$ decays at the optimal rate of $mathcalO(n-1/2)$. For states with finite fourth-order moments, we prove that the relative entropy between $rhoboxplus n$ and $rho_G$ decays at the optimal rate of $mathcalO(n-1)$.
  arXiv  Detail & Related papers  (2024-10-29T12:35:47Z)
• Measuring quantum relative entropy with finite-size effect [53.64687146666141]
  We study the estimation of relative entropy $D(rho|sigma)$ when $sigma$ is known. Our estimator attains the Cram'er-Rao type bound when the dimension $d$ is fixed.
  arXiv  Detail & Related papers  (2024-06-25T06:07:20Z)
• Estimating the Mixing Coefficients of Geometrically Ergodic Markov Processes [5.00389879175348]
  We estimate the individual $beta$-mixing coefficients of a real-valued geometrically ergodic Markov process from a single sample-path. Naturally no density assumptions are required in this setting; the expected error rate is shown to be of order $mathcal O(log(n) n-1/2)$.
  arXiv  Detail & Related papers  (2024-02-11T20:17:10Z)
• On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm [59.65871549878937]
  This paper considers the RMSProp and its momentum extension and establishes the convergence rate of $frac1Tsum_k=1T. Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$. Our convergence rate can be considered to be analogous to the $frac1Tsum_k=1T.
  arXiv  Detail & Related papers  (2024-02-01T07:21:32Z)
• The classical limit of Quantum Max-Cut [0.18416014644193066]
  We show that the limit of large quantum spin $S$ should be understood as a semiclassical limit. We present two families of classical approximation algorithms for $mathrmQMaxCut_S$ based on rounding the output of a semidefinite program to a product of Bloch coherent states.
  arXiv  Detail & Related papers  (2024-01-23T18:53:34Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• On the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$ [0.0]
  We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential $V(r)=-r-1e-C/r$. We derive a simple approximate analytical expression for the eigenvalues for sufficiently small values of the screening parameter $C$.
  arXiv  Detail & Related papers  (2023-09-15T18:34:08Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• $l_{1}$ norm of coherence is not equal to its convex roof quantifier [0.6091702876917281]
  We show that for the widely used coherence measure, $l_1$ norm of coherence $C_l_1$, it holds that $C_l_1neq overlineC_l_1$.
  arXiv  Detail & Related papers  (2021-10-21T04:34:25Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)

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.