Necessary and Sufficient Condition for State-Independent Contextual Measurement Scenarios

摘要

The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (ⅰ) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ⅱ) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number . of the graph χ_f(G) and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.