Operational locality in global theories

Abstract

Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This "it from bit" approach establishes an operational connection between local action and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions.

arXiv comment10+11 pages, 6 figures

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• Categories of Brègman operations and epistemic (co)monads