Contextuality as an External Bookkeeping Cost under Fixed Shared-State Semantics

TL;DR

This paper quantifies the external informational cost of simulating quantum contextuality with classical models, revealing it as an unavoidable bookkeeping expense under fixed shared-state assumptions.

Contribution

It introduces an information-theoretic obstruction cost and establishes a lower bound linking contextuality to external bookkeeping in classical simulations.

Findings

Defines an obstruction cost as mutual information between context and auxiliary label.

Proves a lower bound on this cost using linear witnesses separating observed statistics.

Shows contextuality implies an irreducible external bookkeeping cost in classical models.

Abstract

Contextuality is a central feature distinguishing quantum from classical probability theories, but its operational meaning is often stated only qualitatively. In this Letter, we study a simple information-theoretic question: how much additional contextual information must a classical simulation introduce when it tries to keep a shared internal description fixed across contexts? To make this question precise, we analyze a minimal external-label simulation model in which the remaining context dependence is carried only by an auxiliary label. For this model, we define an obstruction cost as the minimum mutual information between the context and the auxiliary label required to reproduce the observed statistics. We then prove a conservative quantitative lower bound: any linear witness that separates the observed statistics from the zero-obstruction set yields a positive lower bound on this cost. We do not claim that this bound is tight, and we do not claim that the simulation model covers every possible classical architecture. Its role is narrower and more explicit: under fixed shared-state semantics, contextuality can be read as a certificate of irreducible external bookkeeping cost in a simple and well-defined simulation model.