UC Santa Barbara

Motivated by treating the 2 → 1 parity-oblivious multiplexing under the influence of experimental noise, with its success probability serving as an indicator of nonclassicality, this thesis establishes connections between various notions of nonclassicality within the context of what is commonly referred to as the simplest nontrivial scenario (a prepare and measure scenario comprised of four preparations and two binary-outcome tomographically complete measurements). Specifically, we relate the established method developed by Pusey in [20] to witness a violation of preparation noncontextuality, which is not suitable in experiments where the operational equivalences to be tested are specified in advance, with a novel approach based on the notion of bounded ontological distinctness for preparations, defined by Chaturvedi and Saha in [9]. In our approach, we test bounded ontological distinctness for two particular preparations that are relevant in certain information processing tasks in that they are associated with the even- and odd-parity of the bits to be communicated. When there exists an ontological model where this distance is preserved we term this parity preservation. Our main result provides a noise threshold under which violating parity preservation (and so bounded ontological distinctness) agrees with the established method for witnessing preparation contextuality in the simplest nontrivial scenario. This is achieved by first relating the violation of parity preservation to the quantification of contextuality in terms of inaccessible information as developed by Marvian in [17], that we also show, given the way we quantify noise, to be more robust in witnessing contextuality than Pusey’s noncontextuality inequality. As an application of our findings, we treat the case of two-bit parity-oblivious multiplexing in the presence of noise. Specifically, leveraging the identified noise threshold for the existence of preparation contextuality, we establish a condition for which preparation contextuality is present in the case where the probability of success exceeds that achieved by any classical strategy. Overall, our results highlight that, below a certain threshold, all the different methods to witness nonclassicality agree. Consequently, an experimenter can choose the most suitable method based on their specific needs.