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We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programming; it is monotone with respect to the free operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement based quantum computing.
Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, a generalized Spekkens non-contextual ontological model representation of the quantum statistics associated to the prepare-and-measure s
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we pr
Especially investigated in recent years, the Gaussian discord can be quantified by a distance between a given two-mode Gaussian state and the set of all the zero-discord two-mode Gaussian states. However, as this set consists only of product states,
The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJS
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We discuss the possibility for such transitions to charact