Geometrical aspects of weak measurements and quantum erasers

TL;DR

This paper explores the geometric and interference effects in weak measurements using an interferometric approach, highlighting the role of the Pancharatnam phase in the displacement of probe wavepackets.

Contribution

It introduces a unified interferometric framework to analyze weak measurements and quantum erasers, emphasizing the geometric phase's influence on measurement outcomes.

Findings

The Pancharatnam phase arises from post-selection in weak measurements.

Interference patterns are altered by geometric phases.

Displacements in probe wavepackets are linked to the Pancharatnam phase.

Abstract

We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection.