An Information-Theoretic Approach to Contextuality
Classical probabilistic models of quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks. A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality: There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions. In this talk, I discuss a method for quantifying this inaccessible information and present a family of lower bounds on this quantity in terms of experimentally measurable quantities. These bounds, which can also be interpreted as a new class of robust non-contextuality inequalities, are obtained based on a family of guessing games. As an application of this result, I derive a noise threshold for the presence of contextually in a noisy system, in terms of the average gate fidelity of the noise channel.