Minimum uncertainty states and squeezed states from the sum uncertainty relation

TL;DR

This paper investigates the minimum uncertainty states derived from the sum uncertainty relation, comparing them with traditional states, and finds that coherent and squeezed states are unaffected by this new formulation.

Contribution

It demonstrates that minimum uncertainty states for the sum uncertainty relation coincide with those for the product uncertainty relation, clarifying their relationship.

Findings

Minimum uncertainty states for the sum relation are the same as for the product relation.

Coherent and squeezed states remain unaffected by the sum uncertainty relation.

The analysis uses variational methods for position-momentum and angular momentum pairs.

Abstract

Heisenberg uncertainty relation is at the origin of understanding minimum uncertainty states and squeezed states of light. In the recent past, sum uncertainty relation was formulated by Maccone and Pati [Maccone and Pati, Phys. Rev. Lett. 113, 260401 (2014)] which is claimed to be stronger than the existing Heisenberg-Robertson product uncertainty relation. We analyze the minimum uncertainty states for the sum uncertainty relation using the variational approach. We claim that the minimum uncertainty states for the sum uncertainty relation are always the minimum uncertainty states for the traditional product uncertainty relation, using the example of position-momentum pair as well as angular momentum operators. We show that the coherent and squeezed states of radiation remain completely unaffected by the sum uncertainty relation.