The negative probabilities and information gain in weak measurements

TL;DR

This paper investigates weak measurement outcomes, revealing that negative probabilities arise only with minimal information gain and weak coupling, while stronger coupling yields definitive probabilities and eliminates negative values.

Contribution

It provides a theoretical analysis linking negative probabilities in weak measurements to low information gain and coupling strength, clarifying their physical significance.

Findings

Negative probabilities occur only with very weak coupling and low information gain.

Increasing coupling strength allows unambiguous path determination, removing negative probabilities.

Upper bounds for pointer readings in weak measurements are derived.

Abstract

We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative probabilities" emerge in weak measurement. By calculating the information gain of the measuring device about which path the particles pass through, we show that the "negative probabilities" only emerge for cases when the information gain is little due to very weak coupling between the measuring device and the particles. When the coupling strength increases, we can unambiguously determine whether a particle passes through a given path every time, hence the average shifts always represent true probabilities, and the strange "negatives probabilities" disappear.