Simple state preparation for contextuality tests with few observables

TL;DR

This paper investigates conditions under which noncontextuality inequalities can be violated after a simple state preparation involving von Neumann measurements, focusing on the role of initial states and observables.

Contribution

It provides necessary and sufficient conditions for observables that violate noncontextuality inequalities post-preparation, applicable to various initial states and dimensions.

Findings

Existence of observables that violate inequalities depends on initial state eigenvalues.

For states with no zero eigenvalues, such observables always exist.

Conditions are specified for dimensions where inequalities are not always satisfied.

Abstract

We consider any noncontextuality inequality, and the state preparation scheme which consists in performing any von Neumann measurement on any initial state. For an inequality which is not always satisfied, and Hilbert space dimensions greater than a value specified by the inequality, we determine necessary and sufficient conditions for the existence of observables with which the inequality is violated after the preparation process. For an initial state with no zero eigenvalues, there are always such observables, and which are independent of this state.