Operational protocols cannot certify classicality
Chris Fields, James F. Glazebrook, Antonino Marcianò, Emanuele Zappala
TL;DR
The paper proves that no finite, device-independent LOCC protocol can certify separability or classicality of shared quantum states. By modeling LOCC as topologically-local interactions at boundary systems and analyzing the entanglement-entropy measurements through CHSH tests, the authors show that fundamental limits prevent observers from confirming separability or even the location of operational boundaries. They connect these results to prior complexity-theoretic findings, arguing that classicality must remain a pragmatic assumption rather than a verifiable resource. The work reframes classicality as a contextual, intersubjective notion necessary for experimental practice, rather than an objectively certifyable property in quantum theory. This has implications for how we interpret resource theories and the operational verifiability of foundational concepts like separability and classical communication.
Abstract
The existence and practical utility of operational protocols that certify entanglement raises the question of whether operational protocols exist that certify the absence of entanglement, i.e. that certify separability. We show, within a purely topological, interpretation-independent representation, that such protocols do not exist. Classicality is therefore, as Bohr suggested, purely a pragmatic notion.