"Haunted" quantum contextuality

TL;DR

This paper explores a form of quantum contextuality using entangled particles and Kochen-Specker observables, highlighting the challenges in directly measuring contextuality due to its counterfactual nature.

Contribution

It introduces a novel setup involving entangled particles and Kochen-Specker observables to analyze quantum contextuality and discusses the fundamental measurement limitations.

Findings

Quantum contextuality depends on measurement context.

Direct measurement of contextuality is fundamentally impossible.

Counterfactual assumptions are necessary to analyze contextuality.

Abstract

Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables $\{J_1^2,J_2^2,J_3^2\}$ and $\{\bar J_1^2, \bar J_2^2,J_3^2\}$ with $[J_1^2,\bar J_1^2]\neq 0$ are measured. The outcomes of measurements of $J_3^2$ (via $J_1^2,J_2^2$) and $J_3^2$ (via $\bar J_1^2,\bar J_2^2$) are compared. Although formally $J_3^2$ is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether $J_1^2$ or $\bar J_1^2$ is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.