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Various quantum measurement procedures are analyzed and it is shown that under certain conditions they yield consistently {\em weak values} which might be very different from the eigenvalues, the allowed outcomes according to the standard…

Quantum Physics · Physics 2007-05-23 Lev Vaidman

We establish a single-letter characterization of the fundamental distortion-rate-perception tradeoff with limited common randomness under the squared error distortion measure and the squared Wasserstein-2 perception measure. Moreover, it is…

Information Theory · Computer Science 2025-04-25 Xiqiang Qu , Jun Chen , Lei Yu , Xiangyu Xu

Arithmetic, geometric and harmonic means are the three classical means famous in the literature. Another mean such as square-root mean is also known. In this paper, we have constructed divergence measures based on nonnegative differences…

Statistics Theory · Mathematics 2007-06-13 Inder Jeet Taneja

We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…

Quantum Physics · Physics 2012-09-19 Rafal Demkowicz-Dobrzanski , Jan Kolodynski , Madalin Guta

Csiszar's f-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semidefinite matrices are in the place of probability distributions and the quantum…

Information Theory · Computer Science 2015-05-14 Denes Petz

The classical Erd\H{o}s-Tur\'an inequality on the distribution of roots for complex polynomials can be equivalently stated in a potential theoretic formulation, that is, if the logarithmic potential generated by a probability measure on the…

Classical Analysis and ODEs · Mathematics 2021-10-08 Ruiwen Shu , Jiuya Wang

Several inequalities are presented which, in part, generalize inequalities by Weinstein and Weiss, giving rise to new lower bounds for the Bayes risk under squared error loss.

Information Theory · Computer Science 2014-01-22 Asaf Weinstein , Ehud Weinstein

This paper investigates the best known bounds on the quadratic Gaussian distortion-rate-perception function with limited common randomness for the Kullback-Leibler divergence-based perception measure, as well as their counterparts for the…

Information Theory · Computer Science 2024-09-05 Li Xie , Liangyan Li , Jun Chen , Lei Yu , Zhongshan Zhang

The LEP experiment at CERN provided accurate measurements of the $Z$ neutral gauge boson properties. Although all measurements agree well with the SM predictions, the forward backward asymmetry of the bottom-quark remains almost 3$\sigma$…

High Energy Physics - Phenomenology · Physics 2018-03-19 Da Liu , Jia Liu , Carlos E. M. Wagner , Xiao-Ping Wang

The unequal representation of different groups in a sample population can lead to discrimination of minority groups when machine learning models make automated decisions. To address these issues, fairness-aware machine learning jointly…

Machine Learning · Computer Science 2023-11-22 Xuan Zhao , Simone Fabbrizzi , Paula Reyero Lobo , Siamak Ghodsi , Klaus Broelemann , Steffen Staab , Gjergji Kasneci

We develop a QED approach to find the contribution of the quantum vacuum to the electromagnetic Abraham force. Semi-classical theories predict diverging contributions from the quantum vacuum. We show that the divergencies disappear by…

Quantum Physics · Physics 2015-06-04 Bart Van Tiggelen , Sebastien Kawka , Geert L. J. A. Rikken

We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first construction is based on a dynamic variational formulation in…

Differential Geometry · Mathematics 2026-05-27 Martin Bauer , Peter W. Michor , François-Xavier Vialard

We point out that the right-handed squark mixings can sizably enhance SUSY contributions to Delta M_s by taking into account renormalization group effects via the CKM matrix. The recent result of Delta M_s from the D0 experiment at the…

High Energy Physics - Phenomenology · Physics 2009-11-11 Motoi Endo , Satoshi Mishima

An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…

Quantum Physics · Physics 2022-11-21 Michael J. W. Hall

Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science,…

Quantum Physics · Physics 2019-02-27 Bertúlio de Lima Bernardo

We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators. As an application, we explore some consequences of our…

Probability · Mathematics 2024-09-18 Adam Quinn Jaffe , Leonardo V. Santoro

We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based…

Machine Learning · Statistics 2021-10-28 Fan Wu , Patrick Rebeschini

The Berezin--Li--Yau and the Kr\"oger inequalities show that Riesz means of order $\geq 1$ of the eigenvalues of the Laplacian on a domain $\Omega$ of finite measure are bounded in terms of their semiclassical limit expressions. We show…

Spectral Theory · Mathematics 2025-12-09 Rupert L. Frank , Simon Larson , Paul Pfeiffer

We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p \geq 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate whenever the density…

Probability · Mathematics 2024-04-30 Thomas Bonis

We introduce a class of flows on the Wasserstein space of probability measures with finite first moment on the Cartan-Hadamard Riemannian manifold of positive definite matrices, and consider the problem of differentiability of the…

Functional Analysis · Mathematics 2017-05-16 Fumio Hiai , Yongdo Lim