English
Related papers

Related papers: An entropic uncertainty principle for positive ope…

200 papers

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…

Quantum Physics · Physics 2013-11-11 H. S. Karthik , A. R. Usha Devi , J. Prabhu Tej , A. K. Rajagopal

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

Quantum Physics · Physics 2017-06-27 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…

Quantum Physics · Physics 2016-10-12 Shrobona Bagchi , Arun Kumar Pati

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…

Quantum Physics · Physics 2007-10-31 P. Busch , T. Heinonen , P. Lahti

Based on the success of a well-known method for solving higher order linear differential equations, a study of two of the most important mathematical features of that method, viz. the null spaces and commutativity of the product of…

Functional Analysis · Mathematics 2023-12-12 Richard Kadison , Simon Levin , Zhe Liu

The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…

Quantum Physics · Physics 2012-04-24 Chuan-Feng Li , Jin-Shi Xu , Xiao-Ye Xu , Ke Li , Guang-Can Guo

The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…

Quantum Physics · Physics 2016-06-24 F. Adabi , S. Salimi , S. Haseli

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…

Quantum Physics · Physics 2015-05-12 Qiu-Cheng Song , Cong-Feng Qiao

In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…

Quantum Physics · Physics 2016-11-18 Yunlong Xiao , Naihuan Jing , Shao-Ming Fei , Xianqing Li-Jost

Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…

Quantum Physics · Physics 2017-02-09 Patrick J. Coles , Mario Berta , Marco Tomamichel , Stephanie Wehner

We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among…

Quantum Physics · Physics 2013-06-28 Marcelo A. Marchiolli , Paulo E. M. F. Mendonca

We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…

Quantum Physics · Physics 2016-01-19 Y. B. Band , Pier A. Mello

We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…

Quantum Physics · Physics 2016-08-10 Radosław Adamczak , Rafał Latała , Zbigniew Puchała , Karol Życzkowski

In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…

Quantum Physics · Physics 2016-09-19 Luca Nanni

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which…

Mathematical Physics · Physics 2009-11-13 Palle E. T. Jorgensen , Myung-Sin Song

We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…

Functional Analysis · Mathematics 2019-10-31 Darian McLaren , Sarah Plosker , Christopher Ramsey

Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…

Numerical Analysis · Mathematics 2024-11-27 Frank Werner , Bernd Hofmann

Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…

Quantum Physics · Physics 2016-03-16 Varun Narasimhachar , Alireza Poostindouz , Gilad Gour

Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…

Quantum Physics · Physics 2026-04-07 Qing-Hua Zhang , Cong Xu , Jing-Feng Wu , Shao-Ming Fei

The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…

Classical Analysis and ODEs · Mathematics 2018-08-27 Saifallah Ghobber , Philippe Jaming