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Related papers: Tight Entropic Uncertainty Relations

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Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…

Quantum Physics · Physics 2013-05-30 Patrick J. Coles , Roger Colbeck , Li Yu , Michael Zwolak

The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…

Quantum Physics · Physics 2020-10-14 Stephan Sponar , Armin Danner , Kazuma Obigane , Simon Hack , Yuji Hasegawa

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…

Quantum Physics · Physics 2019-04-10 Zhi-Xin Chen , Hui Wang , Jun-Li Li , Qiu-Cheng Song , Cong-Feng Qiao

Uncertainty relations for more than two observables have found use in quantum information, though commonly known relations pertain to a pair of observables. We present novel uncertainty and certainty relations of state-independent form for…

Quantum Physics · Physics 2013-08-19 Alexey E. Rastegin

We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…

Quantum Physics · Physics 2009-11-13 Shengjun Wu , Sixia Yu , Klaus Mølmer

We analyze the uncertainty relation for the sum of variances, which is called in some papers, the stronger uncertainty relation for all incompatible observables. We show that this uncertainty relation for the sum of variances of the…

Quantum Physics · Physics 2025-03-13 K. Urbanowski

Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…

Statistical Mechanics · Physics 2025-11-25 Yoshihiko Hasegawa , Tomohiro Nishiyama

We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…

Quantum Physics · Physics 2010-07-19 Andris Ambainis

Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…

Quantum Physics · Physics 2022-05-25 Yunlong Xiao , Naihuan Jing , Bing Yu , Shao-Ming Fei , Xianqing Li-Jost

Uncertainty relations lie at the very core of quantum mechanics, and form the cornerstone of essentially all quantum cryptographic applications. In particular, they play an important role in cryptographic protocols in the…

Quantum Physics · Physics 2008-08-27 Stephanie Wehner , Andreas Winter

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…

Quantum Physics · Physics 2018-03-08 Chen Qian , Jun-Li Li , Cong-Feng Qiao

Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…

Quantum Physics · Physics 2015-11-20 Zbigniew Puchała , Łukasz Rudnicki , Karol Życzkowski

In the present paper we prove a family of tight upper and lower bounds for the Shannon entropy and von Neumann entropy based on the p-norms. This allows us to have an entropy estimate, a criterion for the finiteness of it and a bound on the…

Information Theory · Computer Science 2024-08-22 Juan Pablo Lopez

Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into…

Quantum Physics · Physics 2017-01-02 Alexey E. Rastegin

We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…

Quantum Physics · Physics 2012-12-07 Cael L. Hasse

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…

Quantum Physics · Physics 2009-11-06 Sumiyoshi Abe , S. Martinez , F. Pennini , A. Plastino

We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to…

Quantum Physics · Physics 2007-05-23 Manuel A. Ballester , Stephanie Wehner

We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions $d = 3$, $4$ and…

We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…

Quantum Physics · Physics 2009-11-10 Otfried Guehne , Maciej Lewenstein

We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the…

Quantum Physics · Physics 2015-06-30 Łukasz Rudnicki , Zbigniew Puchała , Karol Życzkowski