Alladi Ramakrishnan Hall

Lessons for logic and quantum theory from Specker's parable of the overprotective seer

Ravi Kunjwal

IMSc

In this talk I will briefly review a parable that the logician Ernst Specker invented in 1960 to understand the logic of propositions that are not simultaneously decidable. Specker pointed out that the transitivity of implication---that if A => B and B=>C then A=>C---does not hold unless one assumes that the three propositions A, B, and C are simultaneously decidable. Specker then cites the case of propositions about quantum mechanical systems as examples of non-simultaneously decidable propositions. In a modern reformulation of Specker's parable, due to Liang, Spekkens, and Wiseman (LSW, 2011), the authors asked if the sort of scenario that Specker had in mind in posing his parable is realizable in quantum theory when one takes "simultaneous decidability of two propositions" to mean "joint measurability of two observables". They formulate the problem as a noncontextuality inequality, the LSW inequality, and conjecture that it cannot be violated and thus Specker's parable is not realizable in this form. Our result shows how to violate the LSW inequality and demonstrate the Specker's scenario is indeed realizable with nonprojective measurements.

(Based on R. Kunjwal and S. Ghosh, Phys. Rev. A 89, 042118.)