# Noncontextual wirings

## TL;DR

This paper introduces noncontextual wirings as a new class of free operations in the resource theory of contextuality, providing a complete characterization and demonstrating their properties and applications.

## Contribution

It provides the first explicit, physically-motivated class of free operations for contextuality, completing the resource-theoretic framework.

## Key findings

- Relative entropy of contextuality is a monotone.
- Existence of maximally contextual boxes as contextuality bits.
- Complete characterization of noncontextual wirings for black-box devices.

## Abstract

Contextuality is a fundamental feature of quantum theory and is necessary for quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However, the most important component for a resource theory - a concrete, explicit form for the free operations of contextuality - was still missing. Here we provide such a component by introducing noncontextual wirings: a physically-motivated class of contextuality-free operations with a friendly parametrization. We characterize them completely for the general case of black-box measurement devices with arbitrarily many inputs and outputs. As applications, we show that the relative entropy of contextuality is a contextuality monotone and that maximally contextual boxes that serve as contextuality bits exist for a broad class of scenarios. Our results complete a unified resource-theoretic framework for contextuality and Bell nonlocality.