Mixing nonclassical pure states in a linear-optical network almost always generates modal entanglement

TL;DR

This paper demonstrates that almost all nonclassical pure product states input into a linear-optical network produce modal entanglement at the output, except for a specific class of squeezed states, clarifying conditions for entanglement generation.

Contribution

It provides a necessary and sufficient condition for linear-optical networks to generate modal entanglement from pure product states, advancing understanding in quantum optics and boson sampling.

Findings

Almost all nonclassical pure states produce modal entanglement after linear optics.

The only exception is identical squeezed states in a non-mixing network.

This result clarifies when linear networks generate entanglement from pure inputs.

Abstract

In quantum optics a pure state is considered classical, relative to the statistics of photodetection, if and only if it is a coherent state. A different and newer notion of nonclassicality is based on modal entanglement. One example that relates these two notions is the Hong-Ou-Mandel effect, where modal entanglement is generated by a beamsplitter from the nonclassical photon-number state. This suggests that beamsplitters or, more generally, linear-optical networks are mediators of the two notions of nonclassicality. In this Brief Report, we show the following: Given a nonclassical pure-product-state input to an N-port linear-optical network, the output is almost always mode entangled; the only exception is a product of squeezed states, all with the same squeezing strength, input to a network that does not mix the squeezed and anti-squeezed quadratures. Our work thus gives a necessary and sufficient condition for a linear network to generate modal entanglement from pure product inputs, a result that is of immediate relevance to the boson sampling problem.