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Related papers: Uncertainty Principle and Quantum Fisher Informati…

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In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…

General Physics · Physics 2007-07-12 Elias P. Gyftopoulos

Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…

Quantum Physics · Physics 2023-04-25 Stanislaw Kurdzialek , Rafal Demkowicz-Dobrzanski

In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…

Quantum Physics · Physics 2019-08-15 Bing Yu , Naihuan Jing , Xianqing Li-Jost

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…

Probability · Mathematics 2020-06-11 Jeremiah Birrell , Luc Rey-Bellet

We present the uncertainty relations in terms of the symmetrized \r{ho}-absolute variance, which generalizes the uncertainty relations for arbitrary operator (not necessarily Hermitian) to quantum channels. By recalling the quantity…

Quantum Physics · Physics 2024-10-16 Cong Xu , Qing-Hua Zhang , Shao-Ming Fei

Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…

Analysis of PDEs · Mathematics 2020-08-26 Nicolas Rougerie

The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…

Quantum Physics · Physics 2018-03-29 Yu-Xiang Zhang , Shengjun Wu , Zeng-Bing Chen

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show…

Quantum Physics · Physics 2022-11-23 Yakov Bloch , Eliahu Cohen

We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…

Mathematical Physics · Physics 2015-05-30 Rupert L. Frank , Elliott H. Lieb

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…

Quantum Physics · Physics 2018-06-08 Tom Bullock , Paul Busch

A simple proof is given for the monotonicity of entropy and Fisher information associated to sums of i.i.d. random variables. The proof relies on a characterization of maximal correlation for partial sums due to Dembo, Kagan and Shepp.

Information Theory · Computer Science 2016-10-14 Thomas A. Courtade

A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…

Quantum Physics · Physics 2017-01-18 Luigi Seveso , Matteo A. C. Rossi , Matteo G. A. Paris

We revisit, in the framework of Mach-Zehnder interferometry, the connection between the complementarity and uncertainty principles of quantum mechanics. Specifically, we show that, for a pair of suitably chosen observables, the trade-off…

Quantum Physics · Physics 2015-06-05 G. M. Bosyk , M. Portesi , F. Holik , A. Plastino

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…

Quantum Physics · Physics 2015-01-08 Fabian Furrer , Mario Berta , Marco Tomamichel , Volkher B. Scholz , Matthias Christandl

By considering the "kinetic-energy" term of the minimum principle for the Schr\"{o}dinger equation as a measure of information, that minimum principle is viewed as a statistical estimation procedure, analogous to the manner in which Jaynes…

Mathematical Physics · Physics 2007-05-23 John H. Van Drie

Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total and…

Quantum Physics · Physics 2022-08-16 Cong Xu , Zhaoqi Wu , Shao-Ming Fei

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher…

Quantum Physics · Physics 2018-03-20 Sunho Kim , Longsuo Li , Asutosh Kumar , Junde Wu

Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences…

Quantum Physics · Physics 2020-08-12 Diego Paiva Pires , Augusto Smerzi , Tommaso Macrì

The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…

Materials Science · Physics 2025-10-28 Koki Shinada , Naoto Nagaosa

While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…

Quantum Physics · Physics 2007-05-23 Alberto Barchielli , Giancarlo Lupieri