Uncertainty principle and quantum Fisher information. II.

2007/01/31 by P. Gibilisco, Paolo Gibilisco, Daniele Imparato +3 · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wireless Communication Security Techniques #math-ph #math.MP #math.OA

paper · pdf · doi:10.1063/1.2748210

v2, Minor revision. v3, changes made to conform to version accepted on J. Math. Phys

arxiv created 2007/05/21 · openalex publication_date 2007/07/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

Heisenberg and Schrödinger uncertainty principles give lower bounds for the product of variances Varρ(A)Varρ(B) if the observables A,B are not compatible, namely, if the commutator [A,B] is not zero. In this paper, we prove an uncertainty principle in Schrödinger form where the bound for the product of variances Varρ(A)Varρ(B) depends on the area spanned by the commutators i[ρ,A] and i[ρ,B] with respect to an arbitrary quantum version of the Fisher information.

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• Higher entropic uncertainty relations for anti-commuting observables
• Effects of partial measurements on quantum resources and quantum Fisher information of a teleported state in a relativistic scenario