Collision entropy and optimal uncertainty

TL;DR

This paper introduces a new quantum uncertainty measure based on collision entropy for 2D observables, deriving optimal bounds and minimum uncertainty states, and compares it with existing uncertainty principles.

Contribution

It presents an alternative entropic uncertainty relation using collision entropy, providing analytic bounds and identifying minimum uncertainty states in 2D quantum systems.

Findings

Derived the optimal lower bound for the collision entropy-based uncertainty relation.

Obtained the minimum uncertainty states for the 2D case.

Compared the new relation with existing uncertainty formulations.

Abstract

We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results in an analytic function of the overlap of the corresponding eigenbases. Besides, we obtain the minimum uncertainty states. We compare our relation with other formulations of the uncertainty principle.