Quantum contextuality from measurement invasiveness

TL;DR

This paper presents a new framework for analyzing quantum contextuality through invasive measurement models using stochastic linear maps, offering a quantitative measure of contextuality.

Contribution

It introduces a general method to model invasive measurements with linear maps, characterizes their consistency, and quantifies contextuality by minimal invasiveness.

Findings

Identified conditions for admissible invasive measurement maps.

Fully characterized these maps for a three-level quantum system.

Proposed a new quantifier for the degree of contextuality.

Abstract

Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint probability distribution consistent with all measurable contexts, while contextual models violate this condition. Building on this approach, we introduce a general method to analyze contextuality in terms of stochastic linear maps that effectively model invasive measurements on an otherwise classical statistics. These maps transform probabilities within the noncontextuality polytope, which includes all classical probabilities, into probabilities that may lie outside the polytope, while preserving the compatibility structure of the scenario at hand. We derive general consistency conditions that such maps must satisfy to represent admissible invasive measurements, and we fully identify them for a paradigmatic example of contextuality for a single three-level quantum system. Furthermore, we introduce a quantifier of contextuality based on the minimal invasiveness required to reproduce a given probability distribution, which offers a distinct approach on how to evaluate the degree of contextuality in a general scenario.