A complete and operational resource theory of measurement sharpness

Author:

Buscemi Francesco1ORCID,Kobayashi Kodai1,Minagawa Shintaro1ORCID

Affiliation:

1. Department of Mathematical Informatics, Nagoya University, Furo-cho, Chikusa-ku, 464-8601 Nagoya, Japan

Abstract

We construct a resource theory of sharpness for finite-dimensional positive operator-valued measures (POVMs), where the sharpness−non−increasing operations are given by quantum preprocessing channels and convex mixtures with POVMs whose elements are all proportional to the identity operator. As required for a sound resource theory of sharpness, we show that our theory has maximal (i.e., sharp) elements, which are all equivalent, and coincide with the set of POVMs that admit a repeatable measurement. Among the maximal elements, conventional non-degenerate observables are characterized as the canonical ones. More generally, we quantify sharpness in terms of a class of monotones, expressed as the EPR–Ozawa correlations between the given POVM and an arbitrary reference POVM. We show that one POVM can be transformed into another by means of a sharpness-non-increasing operation if and only if the former is sharper than the latter with respect to all monotones. Thus, our resource theory of sharpness is complete, in the sense that the comparison of all monotones provides a necessary and sufficient condition for the existence of a sharpness-non-increasing operation between two POVMs, and operational, in the sense that all monotones are in principle experimentally accessible.

Funder

MEXT Quantum Leap Flagship Progra

MEXT-JSPS Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe”

JSPS KAKENHI

Nagoya University Interdisciplinary Frontier Fellowship

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

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