Generalized fusions of photonic quantum states using static linear optics

TL;DR

This paper numerically investigates advanced fusion measurement techniques in photonic quantum states, introducing ancilla- and code-boosting methods that enhance efficiency but require entangled ancillas, with implications for quantum information processing.

Contribution

It extends fusion measurement schemes with ancilla- and code-boosting, providing a hierarchy of efficiencies and demonstrating the necessity of entanglement for perfect efficiency.

Findings

Hierarchy of fusion efficiencies with up to four single-photon ancillas

Unit efficiency impossible without entangled ancillas

Global measurements can outperform transversal Bell measurements

Abstract

Using numerical simulations, we explore generalized fusion measurements, extending them in three key ways. We incorporate ancilla-boosting and code-boosting to optimize fusion measurements, which may, but do not necessarily, correspond to Bell measurements. For ancilla-boosting beyond Bell measurements, we identify a hierarchy of fusion efficiencies involving up to four single-photon ancillas. From this numerical evidence, we conjecture the efficiencies for a larger number of single-photon ancillas. Interestingly, our findings suggest that achieving unit efficiency is impossible without utilizing entangled ancilla states. Additionally, in the context of code-boosting, we present an example of a global measurement that surpasses the best-known, via transversal Bell measurements achievable efficiency for a small instance of the quantum parity code.