Conditions for Factorizable Output From a Beam splitter

TL;DR

This paper proves that only identical Gaussian states with the same variance produce factorizable, independent output fields when passing through a beam splitter, highlighting a specific condition for uncorrelated outputs.

Contribution

It establishes a precise condition under which Gaussian states yield factorizable outputs from a beam splitter, advancing understanding of quantum state interference.

Findings

Identical Gaussian states with same variance produce factorizable outputs.

Superposition of independent inputs generally yields correlated outputs.

Only identical Gaussian states with equal variance lead to independent outputs.

Abstract

A beam splitter is one of the most important devices in an optics laboratory because of its handiness and versatility; equivalent devices are found in various quantum systems to couple two subsystems or to interfere them. While it is normal that two independent input fields are superposed at the beam splitter to give correlated outputs, identical Gaussian states interfere there to produce totally independent output fields. We prove that Gaussian states with same the variance are the only states which bring about factorizable output fields.