Symmetry-induced failures of tomographic locality: Constructing foil theories by twirling

TL;DR

This paper investigates how symmetries can cause violations of tomographic locality in physical theories, revealing that such failures are common and challenging assumptions in quantum theory axiomatization.

Contribution

It introduces a scheme to generate theories violating tomographic locality by applying symmetry twirling, highlighting the prevalence and implications of these failures.

Findings

Failures of tomographic locality are widespread in twirled theories.

Classical twirled worlds can exhibit nonlocality without ontological holism.

The results question the necessity of superselection rules in quantum theory axiomatization.

Abstract

Tomographic locality is a principle commonly used in the program of finding axioms that pick out quantum theory within the landscape of possible theories. The principle asserts the sufficiency of local measurements for achieving a tomographic characterization of any bipartite state. In this work, we explore the meaning of the principle of tomographic locality by developing a simple scheme for generating a wide variety of theories that violate the principle. In this scheme, one starts with a tomographically local theory -- which can be classical, quantum or post-quantum -- and a physical symmetry, and one restricts the processes in the theory to all and only those that are covariant with respect to the collective action of that symmetry. We refer to the resulting theories as twirled worlds. We show that failures of tomographic locality are ubiquitous in twirled worlds. From the possibility of such failures in classical twirled worlds, we argue that the failure of tomographic locality (i.e., tomographic nonlocality) does not imply ontological holism. Our results also demonstrate the need for researchers seeking to axiomatize quantum theory to take a stand on the question of whether there are superselection rules that have a fundamental status.