Uncertainty equalities and uncertainty relation in weak measurement

TL;DR

This paper derives universal uncertainty equalities for incompatible observables and introduces an uncertainty relation in weak measurement that applies to non-Hermitian operators, enhancing understanding of quantum measurement limitations.

Contribution

It presents new uncertainty equalities valid for all incompatible observables and establishes an uncertainty relation in weak measurement for non-Hermitian operators.

Findings

Derived two universal uncertainty equalities for incompatible observables

Established an uncertainty relation in weak measurement for non-Hermitian operators

Captured limitations on pre- and post-selected ensemble preparation

Abstract

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak measurement which captures the limitation on the preparation of pre- and post-selected ensemble and hold for two non-Hermitian operators corresponding to two non-commuting observables.