Measurement uncertainties in the quantum formalism: quasi-realities of individual systems

TL;DR

This paper explores the implications of operator-based value assignments in quantum measurement uncertainties, linking them to weak values and measurement statistics, and discusses their conceptual significance.

Contribution

It analyzes the conceptual foundations of uncertainty in quantum measurements through the lens of operator-based values and weak measurement theory.

Findings

Operator-based values relate to weak measurement outcomes.

Implications for understanding quantum uncertainties are discussed.

Connections between weak values and measurement uncertainties are clarified.

Abstract

The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for quantum measurements, the correct value of an observable is represented by the operator of that observable. Here, I consider the implications of this operator-based assignment of values to individual systems and discuss the relation with weak values and weak measurement statistics.