Local perception operators and classicality: new tools for old tests

TL;DR

This paper introduces local perception operators (LPOs) as new tools to assess the classicality of quantum states, providing operational criteria that complement traditional Bell tests and can certify local hidden variable models.

Contribution

The authors formalize local perception operators and derive two types of witnesses that offer a new operational perspective on Bell scenarios, focusing on local accessible statistics.

Findings

LPO-based witnesses can certify local hidden variable models.

Criteria depend on local marginals and measurement geometry.

Tools are effective even when Bell violations are inconclusive.

Abstract

Quantum nonlocality is often judged by violations of Bell-type inequalities for a given state. The computation of such violations is a global task, requiring evaluation of global correlations and subsequent testing against a Bell functional. We ask instead: when is a given state local (classical)? We formalize this question via local perception operators (LPOs) that compress global observables into locally accessible statistics, and we derive two complementary witnesses -- one implementable by a single party with classical side information, one intrinsically two-sided. These tools revisit familiar Bell scenarios from a new operational angle. We show how the witness leads to state-aware constraints that depend on local marginals and measurement geometry, with natural specializations to canonical scenarios. The resulting criteria are built from first moments and standard projective measurements and provide a way to certify compatibility with local hidden variable explanations for the LPO-processed data in regimes where conventional Bell violations may be inconclusive.