Geometric formulation of the uncertainty principle

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A geometric approach to formulate the uncertainty principle between quantum observables acting on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the pr...

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Autores principales:	Bosyk, Gustavo Martín, Osán, Tristán Martín, Lamberti, Pedro Walter, Portesi, Mariela
Formato:	article
Lenguaje:	Inglés
Publicado:	2021
Materias:	Uncertainty principle Landau-Pollak inequality Fidelity-based metrics Quantum distances
Acceso en línea:	http://hdl.handle.net/11086/20836 https://doi.org/10.1103/PhysRevA.89.034101
Aporte de:	Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba

id	I10-R14111086-20836
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institution	Universidad Nacional de Córdoba
institution_str	I-10
repository_str	R-141
collection	Repositorio Digital Universitario (UNC)
language	Inglés
topic	Uncertainty principle Landau-Pollak inequality Fidelity-based metrics Quantum distances
spellingShingle	Uncertainty principle Landau-Pollak inequality Fidelity-based metrics Quantum distances Bosyk, Gustavo Martín Osán, Tristán Martín Lamberti, Pedro Walter Portesi, Mariela Geometric formulation of the uncertainty principle
topic_facet	Uncertainty principle Landau-Pollak inequality Fidelity-based metrics Quantum distances
description	A geometric approach to formulate the uncertainty principle between quantum observables acting on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics.
format	article
author	Bosyk, Gustavo Martín Osán, Tristán Martín Lamberti, Pedro Walter Portesi, Mariela
author_facet	Bosyk, Gustavo Martín Osán, Tristán Martín Lamberti, Pedro Walter Portesi, Mariela
author_sort	Bosyk, Gustavo Martín
title	Geometric formulation of the uncertainty principle
title_short	Geometric formulation of the uncertainty principle
title_full	Geometric formulation of the uncertainty principle
title_fullStr	Geometric formulation of the uncertainty principle
title_full_unstemmed	Geometric formulation of the uncertainty principle
title_sort	geometric formulation of the uncertainty principle
publishDate	2021
url	http://hdl.handle.net/11086/20836 https://doi.org/10.1103/PhysRevA.89.034101
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bdutipo_str	Repositorios
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Geometric formulation of the uncertainty principle

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