The uncertainty of quantum states with respect to the projective measurement

TL;DR

This paper systematically characterizes quantum state uncertainty with respect to projective measurements, introduces a universal decomposition, and proposes a new geometric uncertainty measure linked to coherence.

Contribution

It provides a comprehensive framework for understanding quantum uncertainty as an intrinsic property and introduces a novel geometric uncertainty measure.

Findings

Characterization of maximal uncertainty states

Universal decomposition into classical and quantum uncertainty

A new geometric uncertainty measure based on fidelity

Abstract

The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it systematically with respect to given projective measurement. Some basic concepts about uncertainty are reformulated in this context. We prove and get the form of the uncertainty preserving operations. The quantum states with maximal uncertainty are characterized. A universal decomposition of uncertainty into classical uncertainty and quantum uncertainty is provided. Furthermore, a unified and general relation among uncertainty, coherence and coherence of assistance is established. These results are independent of any explicit uncertainty measure. At last, we propose a new uncertainty measure called the geometric uncertainty based on the fidelity and link it with the geometric coherence.