No-broadcasting characterizes operational contextuality

TL;DR

This paper establishes a fundamental link between operational contextuality in quantum information theory and the no-broadcasting theorem, providing a new characterization of quantum states and measurements related to contextuality.

Contribution

It introduces a novel connection between operational contextuality and no-broadcasting, clarifying the conditions under which contextuality arises in quantum states and measurements.

Findings

Contextuality in quantum states is characterized by non-commutativity.

Measurement contextuality is linked to a norm-1 property related to repeatability.

Broadcasting techniques simplify foundational results in contextuality.

Abstract

Operational contextuality forms a rapidly developing subfield of quantum information theory. However, the characterization of the quantum mechanical entities that fuel the phenomenon has remained unknown with many partial results existing. Here, we present a resolution to this problem by connecting operational contextuality one-to-one with the no-broadcasting theorem. The connection works both on the level of full quantum theory and subtheories thereof. We demonstrate the connection in various relevant cases, showing especially that for quantum states the possibility of demonstrating contextuality is exactly characterized by non-commutativity, and for measurements this is done by a norm-1 property closely related to repeatability. Moreover, we show how techniques from broadcasting can be used to simplify known foundational results in contextuality.