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AIP conference proceedings

Pre and post-selection, weak measurements and the flow of time in quantum mechanics

Jeff Tollaksen, Andrei Yu. Khrennikov, Gregg S. Jaeger, Maximilian Schlosshauer, Gregor Weihs

Published Jan 1, 2011• 0 citations
Publisher
DOI
10.1063/1.3578707

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Weak values (WVs) arise from weak measurements performed within a time-symmetric formulation of quantum mechanics, where a system is both pre- and post-selected. Anomalous WVs that lie far outside the eigenvalue spectrum of the observable hold both fundamental and practical significance. However, their generation typically relies on near-orthogonal pre- and post-selection, which confines them to a single post-selection outcome with extremely low success probability. This constraint limits experimental accessibility and hinders the full exploitation of time symmetry. To overcome these limitations, we utilize quantum entanglement and post-selection-controlled operations to generate correlated pairwise two-state vectors. By changing the role of post-selection from passive filtering to active engineering, this approach enables the observation of anomalous complementary WVs associated with mutually exclusive post-selection branches. Our results extend the operational accessibility of time-symmetric quantum structures associated with the two-state vector formalism, and open new avenues for exploring the applications of time symmetry in quantum information processing.
By analysing the concept of contextuality (Bell–Kochen–Specker) in terms of pre- and post-selection, it is possible to assign definite values to observables in a new and surprising way. Physical reasons are presented for restrictions on these assignments. When measurements are performed which do not disturb the pre- and post-selection (i.e. weak measurements), then novel experimental aspects of contextuality can be demonstrated. We also prove that every PPS-paradox with definite predictions directly implies 'quantum contextuality' which is introduced as the analogue of contextuality at the level of quantum mechanics rather than at the level of hidden variable theories. Finally, we argue that certain results of these measurements (e.g. eccentric weak values outside the eigenvalue spectrum) cannot be explained by a 'classical-like' hidden variable theory.