Fidelity matters: the birth of entanglement in the interference of Gaussian states

TL;DR

This paper investigates how the interference of Gaussian states at a beam splitter can generate entanglement, revealing that entanglement depends on the fidelity and purity of the states, with implications for optimizing entanglement creation.

Contribution

It establishes a fidelity threshold criterion for entanglement generation from Gaussian states at a beam splitter, linking entanglement to state purity and transmissivity.

Findings

Entanglement arises if the fidelity between input states is below a certain threshold.

Squeezing is identified as a necessary condition for entanglement.

The results provide a method to optimize entanglement generation using passive optical devices.

Abstract

We address the interaction of two Gaussian states interferring at a beam splitter and analyze the correlations exhibited by the resulting bipartite system. We demonstrate that nonlocal correlations (entanglement) arise if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities and on the transmissivity of the beam splitter. Our result clarifies the role of squeezing as a prerequisite for entanglement and provide a tool to optimize the generation of entanglement by passive devices.