# Scalable symmetry detector and its applications by using beam splitters and weak nonlinearities

## TL;DR

This paper introduces a scalable symmetry detector utilizing beam splitters and weak nonlinearities to identify and purify multiphoton entangled states, enabling efficient detection of multi-pair emissions in quantum optics.

## Contribution

It presents a novel, scalable symmetry detector design that can detect and purify multiphoton entanglement, including multi-pair emissions, with potential applications in quantum information processing.

## Key findings

- Effective detection of four-photon entanglement from SPDC sources.
- Ability to purify entangled states through cascading symmetry detectors.
- Generalization to detect and quantify multi-pair emissions for large photon numbers.

## Abstract

We describe a method to detect twin-beam multiphoton entanglement based on a beam splitter and weak nonlinearities. For the twin-beam four-photon entanglement, we explore a symmetry detector. It works not only for collecting two-pair entangled states directly from the spontaneous parametric down-conversion process, but also for purifying them by cascading these symmetry detectors. Surprisingly, by calculating the iterative coefficient and the success probability we show that with a few iterations the desired two-pair can be obtained from a class of four-photon entangled states. We then generalize the symmetry detector to $n$-pair emissions and show that it is capable of determining the number of the pairs emitted indistinguishably from the spontaneous parametric down-conversion source, which may contribute to explore multipair entanglement with a large number of photons.