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Entropy 2018, 20(6), 454; https://doi.org/10.3390/e20060454

Uncertainty Relations for Coarse–Grained Measurements: An Overview

1
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Brazil
2
Instituto de Física, Universidade Federal Fluminense, Niteroi 24210-346, Brazil
3
Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, Erlangen 91058, Germany
4
Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw 02-668, Poland
*
Author to whom correspondence should be addressed.
Received: 30 April 2018 / Revised: 2 June 2018 / Accepted: 6 June 2018 / Published: 10 June 2018
(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)
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Abstract

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing. View Full-Text
Keywords: quantum uncertainty; quantum foundations; quantum information; continuous variables quantum uncertainty; quantum foundations; quantum information; continuous variables
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Toscano, F.; Tasca, D.S.; Rudnicki, Ł.; Walborn, S.P. Uncertainty Relations for Coarse–Grained Measurements: An Overview. Entropy 2018, 20, 454.

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