# Multimode Entangled States in the Lossy Channel

## TL;DR

This paper analyzes the structure and squeezing properties of highly-entangled multimode states generated by broadband parametric down-conversion, examining measurement schemes and the effects of loss to inform practical quantum computation implementations.

## Contribution

It provides a detailed analysis of supermode structures, compares measurement schemes, and studies squeezing degradation under loss in broadband multimode entangled states.

## Key findings

- Optimal homodyne detection enhances squeezing measurement.
- Lower-complexity detection schemes reduce measured squeezing.
- Photonic loss degrades supermode squeezing significantly.

## Abstract

In this work we analyse the structure of highly-entangled multimode squeezed states, such as those generated by broadband pulses undergoing type-II parametric down-conversion (PDC). Such down-conversion has previously been touted as a natural and efficient means of cluster-state generation, and therefore a viable future pathway to quantum computation. We first detail how broadband PDC processes lead directly to a series of orthogonal supermodes that are linear combinations of the original frequency modes. We then calculate the total squeezing of the multimode entangled states when they are assumed to be measured by an ideal homodyne detection in which all supermodes of the states are detected by an optimally shaped local oscillator (LO) pulse. For comparison, squeezing of the same entangled states are calculated when measured by a lower-complexity homodyne detection scheme that exploits an unshaped LO pulse. Such calculations illustrate the cost, in the context of squeezing, of moving from higher complexity (harder to implement) homodyne detection to lower-complexity (easier-to-implement) homodyne detection. Finally, by studying the degradation in squeezing of the supermodes under photonic loss, multimode entangled state evolution through an attenuation channel is determined. The results reported here push us towards a fuller understanding of the real-world transfer of cluster-states when they take the form of highly-entangled multimode states in frequency space.