# Generating entanglement with linear optics

## TL;DR

This paper investigates the fundamental limits and optimal schemes for generating entanglement using linear optics, revealing constraints on Bell state creation and entanglement bounds in various optical configurations.

## Contribution

It proves Bell states cannot be generated with only 3 photons in dual-rail encoding and provides numerical evidence for the optimality of 4-photon schemes, exploring entanglement limits in different setups.

## Key findings

- Bell states cannot be generated with 3 photons in dual-rail encoding
- Numerical evidence supports the optimality of 4-photon schemes
- Constant bounds on entanglement exist despite increasing photon numbers

## Abstract

Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only 3 photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing 4 photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.