On a generalized entropic uncertainty relation in the case of the qubit

We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We...

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Detalles Bibliográficos
Autores principales:	Zozor, Steeve, Bosyk, Gustavo Martín, Portesi, Mariela Adelina
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2013
Materias:	Física Foundations of quantum mechanics; measurement theory Entropy and other measures of information Formalism Quantum systems with finite Hilbert space
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/132336
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-132336
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Física Foundations of quantum mechanics; measurement theory Entropy and other measures of information Formalism Quantum systems with finite Hilbert space
spellingShingle	Física Foundations of quantum mechanics; measurement theory Entropy and other measures of information Formalism Quantum systems with finite Hilbert space Zozor, Steeve Bosyk, Gustavo Martín Portesi, Mariela Adelina On a generalized entropic uncertainty relation in the case of the qubit
topic_facet	Física Foundations of quantum mechanics; measurement theory Entropy and other measures of information Formalism Quantum systems with finite Hilbert space
description	We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of Rényi entropies for any couple of (positive) entropic indices (α,β). Thus, we have overcome the Holder conjugacy constraint imposed on the entropic indices by Riesz–Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0, 1/2]2 in the α–β plane, and a semi-analytical expression on the line β = α. It is seen that previous results are included as particular cases. Moreover we present a semi-analytical, suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.
format	Articulo Articulo
author	Zozor, Steeve Bosyk, Gustavo Martín Portesi, Mariela Adelina
author_facet	Zozor, Steeve Bosyk, Gustavo Martín Portesi, Mariela Adelina
author_sort	Zozor, Steeve
title	On a generalized entropic uncertainty relation in the case of the qubit
title_short	On a generalized entropic uncertainty relation in the case of the qubit
title_full	On a generalized entropic uncertainty relation in the case of the qubit
title_fullStr	On a generalized entropic uncertainty relation in the case of the qubit
title_full_unstemmed	On a generalized entropic uncertainty relation in the case of the qubit
title_sort	on a generalized entropic uncertainty relation in the case of the qubit
publishDate	2013
url	http://sedici.unlp.edu.ar/handle/10915/132336
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bdutipo_str	Repositorios
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On a generalized entropic uncertainty relation in the case of the qubit

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