Tight Bounds from Multiple‐Observable Entropic Uncertainty Relations

Riccardi, Alberto; Chesi, Giovanni; Macchiavello, Chiara; Maccone, Lorenzo

doi:10.1002/andp.202400020

Tight Bounds from Multiple‐Observable Entropic Uncertainty Relations

Journal Article · Thu May 23 04:00:00 EDT 2024 · Annalen der Physik (Leipzig)

DOI:https://doi.org/10.1002/andp.202400020· OSTI ID:2429045

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INFN Sezione di Pavia Via Agostino Bassi 6 Pavia I‐27100 Italy
INFN Sezione di Pavia Via Agostino Bassi 6 Pavia I‐27100 Italy, Dipartimento di Fisica Università degli Studi di Pavia Via Agostino Bassi 6 Pavia I‐27100 Italy

Abstract

The additivity properties for both bipartite and multipartite systems are investigated by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular, state‐independent and state‐dependent entropic inequalities are introduced. Interestingly, the violation of these inequalities is strictly connected with the presence of quantum correlations. It is shown that the additivity of EUR holds only for EUR that involve two observables, while this is not the case for inequalities that consider more than two observables or the addition of the von Neumann entropy of a subsystem. They are applied to bipartite systems and to several classes of states of a three‐qubit system.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

Grant/Contract Number:: NONE; AC02-07CH11359

OSTI ID:: 2429045

Journal Information:: Annalen der Physik (Leipzig), Journal Name: Annalen der Physik (Leipzig) Journal Issue: 8 Vol. 536; ISSN 0003-3804

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: Germany

Language:: English

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