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Related papers: Uncertainty Principle and Quantum Fisher Informati…

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We show that two quantities in quantum metrology that were thought to be the same, the quantum Fisher information matrix and the Bures metric, are not the same. They differ at points at which the rank of the density matrix changes. The…

Quantum Physics · Physics 2017-05-17 Dominik Šafránek

This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…

General Relativity and Quantum Cosmology · Physics 2009-10-22 J. J. Halliwell

We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty…

Quantum Physics · Physics 2021-11-18 Qing-Hua Zhang , Shao-Ming Fei

Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew…

Quantum Physics · Physics 2020-04-27 Zhaoqi Wu , Lin Zhang , Jianhui Wang , Xianqing Li-Jost , Shao-Ming Fei

We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic…

Quantum Physics · Physics 2015-01-13 Marcin Jarzyna , Rafal Demkowicz-Dobrzanski

A generalisation of the classical covariance for quantum mechanical observables has previously been presented by Gibilisco, Hiai and Petz. Gibilisco and Isola has proved that the usual quantum covariance gives the sharpest inequalities for…

Mathematical Physics · Physics 2017-08-24 Attila Lovas , Attila Andai

The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…

Quantum Physics · Physics 2019-12-03 H. Dolatkhah , S. Haseli , S. Salimi , A. s. Khorashad

Measurement error and disturbance, in the presence of conservation laws, are analysed in general operational terms. We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements…

Quantum Physics · Physics 2023-06-07 M. Hamed Mohammady , Takayuki Miyadera , Leon Loveridge

We prove that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all classical interactions derived from systems of particles.…

Analysis of PDEs · Mathematics 2024-09-04 Cyril Imbert , Luis Silvestre , Cédric Villani

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum…

Quantum Physics · Physics 2010-01-10 S. Furuichi , K. Yanagi , K. Kuriyama

Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…

Quantum Physics · Physics 2010-04-28 Masanao Ozawa

Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…

Information Theory · Computer Science 2022-07-12 Jiannan Yang

The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…

Quantum Physics · Physics 2024-12-19 Kyoung Yeon Kim

Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…

Statistical Mechanics · Physics 2007-05-23 Piotr Garbaczewski

We demonstrate that quantum Fisher information and superradiance can be formulated as coherence measures in accordance with the resource theory of coherence, thus establishing a direct link between metrological information, superradiance…

Quantum Physics · Physics 2018-05-09 Kok Chuan Tan , Seongjeon Choi , Hyukjoon Kwon , Hyunseok Jeong

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…

Quantum Physics · Physics 2011-12-08 Patrick J. Coles , Li Yu , Michael Zwolak

Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and…

Quantum Physics · Physics 2021-08-06 Huaijing Huang , Zhaoqi Wu , Shao-Ming Fei

Chentsov studied Riemannian metrics on the set of probability measures from the point of view of decision theory. He proved that up to a constant factor the Fisher information is the only metric which is monotone under stochastic…

Quantum Physics · Physics 2007-05-23 D. Petz , Cs. Sudar

Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$ det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j])) $$ gives a bound for the quantum generalized…

Mathematical Physics · Physics 2009-11-13 P. Gibilisco , D. Imparato , T. Isola

The variance of quantum channels involving a mixed state gives a hybrid of classical and quantum uncertainties. We seek certain decomposition of variance into classical and quantum parts in terms of the Wigner-Yanase skew information.…

Quantum Physics · Physics 2023-12-21 Qing-Hua Zhang , Jing-Feng Wu , Shao-Ming Fei