Linear-Optical Hyperentanglement-Assisted Quantum Error-Correcting Code

TL;DR

This paper presents a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code that uses photonic states entangled in polarization and orbital angular momentum to correct polarization flip errors.

Contribution

It introduces a novel hyperentanglement-assisted quantum error-correcting code implemented with linear optics, enabling error correction using minimal ancilla modes.

Findings

Successful encoding and decoding with a unit-fidelity circuit

Achieves a success probability of 0.0097

Uses hyperentanglement in polarization and orbital angular momentum

Abstract

We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and orbital angular momentum. It is possible to encode, decode, and diagnose channel errors using linear-optical techniques. The code corrects for polarization "flip" errors and is thus suitable only for a proof-of-principle experiment. The encoding and decoding circuits use a Knill-Laflamme-Milburn-like scheme for transforming polarization and orbital angular momentum photonic qubits. A numerical optimization algorithm finds a unit-fidelity encoding circuit that requires only three ancilla modes and has success probability equal to 0.0097.