Simple rules for two-photon state preparation with linear optics

TL;DR

This paper provides a comprehensive characterization of two-photon entangling operations using linear optics, identifying conditions for state preparation, auxiliary photon requirements, and constructing multi-qubit gates for quantum information processing.

Contribution

It introduces a matrix-based framework to determine when two-photon entanglement is possible with linear optics and offers methods for arbitrary state preparation and multi-qubit gate construction.

Findings

Derived necessary and sufficient conditions for two-photon entangling operations.

Characterized input states for arbitrary two-qudit state preparation.

Established photon requirements for heralded state preparation.

Abstract

Entangling photons is a critical challenge for photonic quantum information processing: entanglement is a crucial resource for quantum communication and computation but can only be performed in a probabilistic manner when using linear optics. In this work, we leverage a two-photon state matrix representation to derive necessary and sufficient conditions on two-photon entangling operations with linear optics. We give a characterization of the input photonic states that can be used to prepare arbitrary two-qudit states in d-rail encoding with post-selection. We determine how many auxiliary photons are required to prepare any two-photon state with heralding. In addition, we present a construction for generalized post-selected n-qubit control-rotation gates.