On the equivalence between squeezing and entanglement potential for two-mode Gaussian states

TL;DR

This paper demonstrates that for all two-mode Gaussian states, the entanglement potential achievable through passive transformations is equivalent to their squeezing of formation, uniting two key quantum resource theories.

Contribution

The authors introduce a new class of states that saturate the entanglement potential bound and conjecture all two-mode Gaussian states can be transformed into this class.

Findings

A larger class of states saturates the entanglement potential bound.

Numerical evidence supports the conjecture that all two-mode Gaussian states can be transformed into this class.

Passive transformations can be explicitly constructed to achieve this equivalence.

Abstract

The maximum amount of entanglement achievable under passive transformations by continuous-variable states is called the entanglement potential. Recent work has demonstrated that the entanglement potential is upper-bounded by a simple function of the squeezing of formation, and that certain classes of two-mode Gaussian states can indeed saturate this bound, though saturability in the general case remains an open problem. In this study, we introduce a larger class of states that we prove saturates the bound, and we conjecture that all two-mode Gaussian states can be passively transformed into this class, meaning that for all two-mode Gaussian states, entanglement potential is equivalent to squeezing of formation. We provide an explicit algorithm for the passive transformations and perform extensive numerical testing of our claim, which seeks to unite the resource theories of two characteristic quantum properties of continuous-variable systems.