Photon catalysis for general multimode multi-photon quantum state preparation

TL;DR

This paper presents a novel method for generating any multimode multi-photon quantum state using photon catalysis, multiport interferometers, and advanced algebraic techniques, achieving perfect fidelity.

Contribution

It introduces a new approach linking quantum state engineering with symmetric tensor decomposition, enabling exact state preparation with minimal catalysis photons.

Findings

Achieves 100% fidelity in state generation

Provides a systematic procedure for arbitrary multimode states

Demonstrates superiority over existing methods in benchmarks

Abstract

Multimode multiphoton states are at the center of many photonic quantum technologies, from photonic quantum computing to quantum sensing. In this work, we derive a procedure to generate exactly, and with a predictable number of steps, any such state by using only multiport interferometers, photon number resolving detectors, photon additions and displacements. We achieve this goal by establishing a connection between photonic quantum state engineering and the algebraic problem of symmetric tensor decomposition. This connection allows us to solve the problem by using corresponding results from algebraic geometry and unveils a mechanism of photon catalysis, where photons are injected and subsequently retrieved in measurements, to generate entanglement that cannot be obtained through Gaussian operations. We also introduce a tensor decomposition, that generalizes our method and allows to construct circuits yielding perfect fidelity, using the minimum number of catalysis photons. As a benchmark, we numerically evaluate our method and compare its performance with state-of-the art results, confirming 100\% fidelity on different classes of states.