Dr Andrei Constantin

Abstract:

The contextual fraction introduced by Abramsky and Brandenburger defines a quantitative measure of contextuality associated with empirical models, i.e. tables of probabilities of measurement outcomes in experimental scenarios. In this paper we define an entanglement monotone relying on the contextual fraction. We first show that any separable state is necessarily non-contextual with respect to any Bell scenario. Then, for 2-qubit states, we associate a state-dependent Bell scenario and show that the corresponding contextual fraction is an entanglement monotone, suggesting contextuality may be regarded as a refinement of entanglement. We call this monotone the quarter-turn contextual fraction, and use it to set an upper bound of approximately 0.601 for the minimum entanglement entropy needed to guarantee contextuality with respect to some Bell scenario.

Abstract:

We determine several classes of smooth complex projective surfaces on which Zariski decomposition can be combined with vanishing theorems to yield cohomology formulae for all line bundles. The obtained formulae express cohomologies in terms of divisor class intersections, and are adapted to the decomposition of the effective cone into Zariski chambers. In particular, we show this occurs on generalised del Pezzo surfaces, toric surfaces, and K3 surfaces. In the second part we use these surface results to derive formulae for all line bundle cohomology on a simple class of elliptically fibered Calabi–Yau three-folds. Computing such quantities is a crucial step in deriving the massless spectrum in string compactifications.