When a negative weak value -1 plays the counterpart of a probability 1

TL;DR

This paper demonstrates that a negative weak value of -1 can be physically interpreted as a counterpart to a probability of 1, confirmed through photon experiments showing symmetrical polarization shifts.

Contribution

The study provides the first direct physical interpretation of negative weak values as counterparts to probabilities, verified experimentally with photon polarization shifts.

Findings

Negative weak value of -1 corresponds to a symmetrical polarization shift.

Experimental verification using photon interference confirms the physical effect.

Weak value effects are observable as polarization rotations, not just ensemble averages.

Abstract

When the weak value of a projector is 1, a quantum system behaves as in that eigenstate with probability 1. By definition, however, the weak value may take an anomalous value lying outside the range of probability like -1. From the viewpoint of a physical effect, we show that such a negative weak value of -1 can be regarded as the counterpart of the ordinary value of 1. Using photons, we experimentally verify it as the symmetrical shift in polarization depending on the weak value given by pre-postselection of the path state. Unlike observation of a weak value as an ensemble average via weak measurements, the effect of a weak value is definitely confirmed in two photon interference: the symmetrical shift corresponding to the weak value can be directly observed as the rotation angle of a half wave plate.