title: Necessary and sufficient condition for state-independent contextual measurement scenarios.
abstract: 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 χf(G) and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.
authors.affiliation: National Quantum Information Center of Gdansk, 81-824 Sopot, Poland and University of Gdansk, 80-952 Gdansk, Poland.
authors.forename: Ravishankar
authors.initials: R
authors.lastname: Ramanathan
authors.affiliation: National Quantum Information Center of Gdansk, 81-824 Sopot, Poland and Faculty of Applied Physics and Mathematics, Technical University of Gdansk, 80-233 Gdansk, Poland.
authors.forename: Pawel
authors.initials: P
authors.lastname: Horodecki