State independent uncertainty relations from eigenvalue minimization

TL;DR

This paper introduces a method for deriving uncertainty relations using eigenvalue minimization of Hamiltonians, simplifying the process of finding lower bounds on the sum of variances for multiple observables.

Contribution

The paper presents a novel eigenvalue minimization approach to obtain uncertainty bounds, applicable to various observables, streamlining the derivation process.

Findings

Method effectively finds lower bounds for multiple observables.

Applicable to both bounded and unbounded operators.

Demonstrated on known and new uncertainty relation cases.

Abstract

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the many known techniques developed to this aim. To demonstrate the simplicity of the method we analyze multiple instances, both previously known and novel, that involve two or more observables, both bounded and unbounded.