Purity and Gaussianity bounded uncertainty relation

TL;DR

This paper derives an analytical uncertainty relation constrained by purity and Gaussianity, unifying previous bounds and providing a new perspective on quantum state uncertainties.

Contribution

It introduces a novel uncertainty relation bounded by purity and Gaussianity, extending and unifying prior bounds in quantum uncertainty research.

Findings

Derived an analytical uncertainty relation with purity and Gaussianity constraints

Reproduces previous purity-bounded and Gaussianity-bounded uncertainty relations as special cases

Provides a unified framework for quantum state uncertainty bounds

Abstract

Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity. In a limiting case this uncertainty relation reproduces the purity-bounded derived by V I Man'ko and V V Dodonov and the Gaussianity-bounded one [Phys. Rev. A 86, 030102R (2012)].