Interactions of pre- and postselected quantum particles

TL;DR

This paper develops a TSVF-based framework to analyze effective interactions between pre- and postselected quantum particles by treating presence as a local trace quantified by weak values of projections and their products. It distinguishes pure weak values (complete pre- and postselection) from mixed weak values (incomplete postselection or entanglement) and shows how joint weak values modify interparticle couplings, including cases where product rules fail. The authors apply the formalism to paradoxes such as the three-box and pigeonhole scenarios and to electron-attraction experiments, illustrating amplification, reversal, and counterintuitive presence results. The work offers a unified, operational perspective on pre- and postselected systems with potential implications for foundations and precision quantum control.

Abstract

An approach for analysis of effective interaction between pre- and postselected quantum particles is developed. It is argued that the cases of complete pre- and postselection of particles are more profound than the cases of partial pre- and postselection, since the former goes beyond modification of the average of interactions on an ensemble of experiments. Recently discussed paradoxical phenomena such as the pigeonhole paradox and the modification of the interaction from repulsion to attraction are analyzed within the introduced formalism, and a few new surprising examples are presented.

Figures (3)

• Figure 1: Scenarios of Particle Presence. a) The particle does not pass through the interferometer. b) The particle passes through arm $A$. This corresponds to the preselection of state $|A\rangle$ just before the interaction region and the postselection of the same state $|A\rangle$ shortly afterward. c) The particle is described by a superposition of interferometric paths/arms. The entry in a particular input port of the interferometer and the detection in the particular output port are equivalent to pre- and postselection states of the form (\ref{['setup-pre']}) and (\ref{['setup-post']}) at an intermediate time.
• Figure 2: Two Mach-Zehnder Interferometers with interaction between particles in part of arm $A$. Two particles distinguishable by their transverse location pass simultaneously through interferometers close enough to have an observable interaction between them. The transverse distance between the particles is much larger than the their transverse uncertainty.
• Figure 3: Single Mach-Zehnder Interferometer with interaction between particles in both arms. Two electrons distinguishable by their transverse location pass simultaneously through a Mach-Zehnder interferometer close enough to have observable interaction between them. They interact in arm A and in arm B.