Revealing quantum contextuality using a single measurement device

In this work we analyse the notion of measurement non-contextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. We show that any non-contextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive operator valued measure (POVM) executed sequentially on a quantum system. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual (NC) ontic model, and construct a quantum situation involving measurements from the KCBS inequality. We show that the resultant statistics arising from this device violate our NC inequality. This device can be generalised by incorporating measurements from arbitrary $n$-cycle contextuality inequalities of which $n = 5$ corresponds to the KCBS inequality. We show that the NC and quantum bounds for various scenarios can be derived more easily using only the functional relationships between the outcomes for larger values $n$. This makes it one of the simpler contextual inequalities to analyse.

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