A unique quasi-probability for projective yes-no measurements

TL;DR

This paper introduces a unique quasi-probability for projective yes-no measurements, derived from fundamental principles, and explores its properties, including its nonclassicality and relation to weak measurements.

Contribution

It identifies a unique operational quasi-probability for projective measurements based on invariance principles and derives its complex extension, advancing understanding of measurement disturbance.

Findings

Wigner rule is the unique quasi-probability for post-measurement states

A pre-measurement quasi-probability is derived from invariance principles

The quasi-probability's nonclassicality stems from measurement disturbance

Abstract

From an analysis of projective measurements, it is shown that the Wigner rule is the unique operational quasi-probability for the post-measurement state. A unique pre-measurement quasi-probability is derived from a principle of invariance of measurement disturbance under orthogonal projector complementation. Physical arguments for this principle are given. The informationally complete complex extension of the quasi-probability is also derived. Nonclassicality of this quasi-probability is due to measurement disturbance. The same quasi-probability follows from weak measurements.