# Generation of Large Number-Path Entanglement Using Linear Optics and Feed-Forward

## TL;DR

This paper presents a linear optics and feed-forward method to efficiently generate large N00N states and Schrödinger cat states, with exponential scalability, for applications in quantum imaging and metrology.

## Contribution

It introduces an idealised measurement and feed-forward scheme to produce large number-path entanglement states with improved scalability over previous methods.

## Key findings

- High-probability routing of photons using partial detection
- Generation of Schrödinger cat states through dual-port detection
- Exponential scalability compared to existing proposals

## Abstract

We show how an idealised measurement procedure can condense photons from two modes into one, and how, by feeding forward the results of the measurement, it is possible to generate efficiently superpositions of components for which only one mode is populated, commonly called ``N00N states''. For the basic procedure, sources of number states leak onto a beam splitter, and the output ports are monitored by photodetectors. We find that detecting a fixed fraction of the input at one output port suffices to direct the remainder to the same port with high probability, however large the initial state. When instead photons are detected at both ports, Schr\"{o}dinger cat states are produced. We describe a circuit for making the components of such a state orthogonal, and another for subsequent conversion to a N00N state. Our approach scales exponentially better than existing proposals. Important applications include quantum imaging and metrology.