No contextual advantage in non-paradoxical scenarios of two state vector formalism

Abstract

The two state vector formalism (TSVF) was proposed by Aharonov, Bergmann, and Lebowitz (ABL) to provide a way for the counterfactual assignment of the probabilities of outcomes of contemplated but unperformed measurements on quantum systems. This formalism underlies various aspects of foundations of quantum theory and has been used significantly in the development of weak values and several proofs of quantum contextuality. We consider the application of TSVF, with pre- and post-selection (PPS) and the corresponding ABL rule, as a means to unearth quantum contextuality. We use the principle of exclusivity to classify the resultant pre- and post-selection scenarios as either paradoxical or non-paradoxical. In light of this, we find that several previous proofs of the emergence of contextuality in PPS scenarios are only possible if the principle of exclusivity is violated and are therefore classified as paradoxical. We argue that these do not constitute a proper test of contextuality. Furthermore, we provide a numerical analysis for the KCBS scenario as applied in the paradigm of TSVF and find that non-paradoxical scenarios do not offer any contextual advantage. Our approach can be easily generalized for other contextual scenarios as well.