|DATE||April 02 (Mon), 2018|
|TITLE||Logical and inequality based contextuality for qudits and a proposed experiment to test the ontological faithful non-contextuality|
In this work I will present a generalization of the recently developed Hardy-like logical proof ofcontextuality and of the so-called KCBS contextuality inequality for any qudit of dimension greaterthan three that we have developed Our approach uses compatibility graphs that can only be satisfied by qudits. Wefind a construction for states and measurements that satisfy these graphs and demonstrate bothlogical and inequality based contextuality for qudits. Interestingly, the quantum violation of theinequality is constant as dimension increases. We also discuss the issue of imprecision in experimentalimplementations of contextuality tests and a way of addressing this problem using the notion ofontological faithfulness. We propose a method to experimentally test ontological faithful non-contextuality with our family of contextuality tests for qudits. The experiment we propose is to use a qudit encoded inthe path of a single photon and its temporal properties. Our idea is based on previous experimentalobservation of contextuality with the KCBS inequality. We also make a practical interpretationof the ontological faithful non-contextuality that permits to bound the precision of the experimental setup that used the path and time properties of a single photon under which ontologicalfaithful non-contextual model is refuted. The noise tolerance is also compared for different types ofdecoherence models and different types of encoding of qudits.