English
Related papers

Related papers: Entropic uncertainty relations for SIC-POVMs and M…

200 papers

Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…

Statistical Mechanics · Physics 2025-04-09 Jonas H. Fritz , Benjamin Ertel , Udo Seifert

In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the "uncertainty regions'' given by all vectors, whose components are specified by the variances of the three…

Quantum Physics · Physics 2015-10-05 Lars Dammeier , René Schwonnek , Reinhard F. Werner

Quantum measurements play a fundamental role in quantum information. Therefore, increasing efforts are being made to construct symmetric measurement operators for qudit systems. A wide class of projective measurements corresponds to complex…

Quantum Physics · Physics 2026-01-06 Katarzyna Siudzińska

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…

Quantum Physics · Physics 2015-02-24 Petr Jizba , Jacob A. Dunningham , Jaewoo Joo

We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…

Quantum Physics · Physics 2017-04-17 Jun Zhang , Yang Zhang , Chang-shui Yu

We discuss the relationship between entropic Einstein-Podolsky-Rosen (EPR)-steering inequalities and their underlying uncertainty relations, along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering…

Quantum Physics · Physics 2014-03-04 James Schneeloch , Curtis J. Broadbent , John C. Howell

We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…

Quantum Physics · Physics 2018-01-16 Anaelle Hertz , Michael G. Jabbour , Nicolas J. Cerf

We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…

Quantum Physics · Physics 2016-01-18 Reinhard F. Werner

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…

Quantum Physics · Physics 2017-05-25 Qiu-Cheng Song , Jun-Li Li , Guang-Xiong Peng , Cong-Feng Qiao

Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…

Probability · Mathematics 2023-03-06 Daniel Lazarev

We investigate the uncertainty principle for two successive projective measurements in terms of R\'enyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty…

Quantum Physics · Physics 2015-04-14 Jun Zhang , Yang Zhang , Chang-shui Yu

We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure…

Quantum Physics · Physics 2011-12-23 O. Jiménez , M. A. Solís-Prosser , A. Delgado , L. Neves

We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of…

Quantum Physics · Physics 2012-11-06 Łukasz Rudnicki , Stephen P. Walborn , Fabricio Toscano

We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the…

Quantum Physics · Physics 2018-12-20 Tamás Kriváchy , Florian Fröwis , Nicolas Brunner

We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…

Quantum Physics · Physics 2007-05-23 Dominic W. Berry , Barry C. Sanders

Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…

Quantum Physics · Physics 2009-11-13 Iwo Bialynicki-Birula

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Machine Learning · Statistics 2023-02-22 Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We…

Quantum Physics · Physics 2015-08-25 Lu Liu , Ting Gao , Fengli Yan

We obtain uncertainty and certainty relations of state-independent form for the three Pauli observables with use of the R\'enyi entropies of order $\alpha\in(0;1]$. It is shown that these entropic bounds are tight in the sense that they are…

Quantum Physics · Physics 2014-04-03 Alexey E. Rastegin

We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…

Quantum Physics · Physics 2025-11-27 Jiaxi Kuang , Kensei Torii , Francesco Buscemi