No contextual advantage in nonparadoxical scenarios of the two-state vector formalism

Abstract

The two-state vector formalism (TSVF) proposed by Aharonov, Bergmann, and Lebowitz [A. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964)] allows a counterfactual assignment of probabilities of outcomes of contemplated (but unperformed) measurements on quantum systems. The probabilities assigned by the Aharonov-Bergmann-Lebowitz (ABL) rule and the associated weak values have been used to provide insights into quantum situations and to unearth underlying quantum contextuality. We apply the principle of exclusivity on ABL probabilities which are assigned to mutually orthogonal projectors to define paradoxical and nonparadoxical scenarios. Given a pre- and a postselected pair of states, we consider the nonparadoxical sector with a view to explore the demonstration of quantum contextuality. For the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky scenario, we numerically show that the ABL probabilities of the TSVF in the nonparadoxical sector do not offer any contextual advantage. Our approach can be easily generalized to other contextual scenarios as well. We thus argue that several previous proofs of the emergence of contextuality in pre- and postselected scenarios are only possible if the principle of exclusivity is violated and are therefore classified as paradoxical.