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

Jeff Tollaksen, Andrei Yu. Khrennikov, Gregg S. Jaeger +2 more

Qian Xie, Liang Xu, Lijian Zhang

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.

D. J. Miller

Jeff Tollaksen

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.

Julius Ruseckas, B. Kaulakys

Jeff Tollaksen

The two-state vector formalism provides a complete description of pre- and post-selected quantum systems and has uncovered a host of new quantum phenomena which were previously hidden. The most important feature is that any weak coupling to a pre- and post-selected system is effectively a coupling to a "weak value" which is given by a simple expression depending on the two-state vector. In particular, weak values, are the outcomes of so called "weak measurements" which have recently become a very powerful tool for ultra-sensitive measurements. Using weak values, I will show that the classical limit of quantum mechanics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects.