Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures

Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures

We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner prod...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Vol. 90; no. 5
Main Authors: Bosyk, G. M., Zozor, S., Portesi, M., Osán, T. M., Lamberti, P. W.
Format: Journal Article
Language:English
Published: American Physical Society 19-11-2014
Subjects:
Computer Science
Information Theory
Mathematical Physics
Physics
Quantum Physics
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Summary:We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau-Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.90.052114