Heralded creation of photonic qudits from parametric down conversion using linear optics

TL;DR

This paper presents a heralded method to generate arbitrary quantum superpositions of two-mode optical states with fixed photon number, enabling creation of photonic qudits and applications in quantum error correction.

Contribution

The authors introduce a novel experimental scheme for heralded generation of photonic qudits using linear optics and parametric down conversion, demonstrated for the case of n=2.

Findings

Successfully demonstrated generation of qutrit states via homodyne tomography

Calculated examples of NOON states and error-correcting logical qubits

Scheme enables bosonic qubit error correction with reduced photon loss

Abstract

We propose an experimental scheme to generate, in a heralded fashion, arbitrary quantum superpositions of two-mode optical states with a fixed total photon number $n$ based on weakly squeezed two-mode squeezed state resources (obtained via weak parametric down conversion), linear optics, and photon detection. Arbitrary $d$-level (qudit) states can be created this way where $d=n+1$. Furthermore, we experimentally demonstrate our scheme for $n=2$. The resulting qutrit states are characterized via optical homodyne tomography. We also discuss possible extensions to more than two modes concluding that, in general, our approach ceases to work in this case. For illustration and with regards to possible applications, we explicitly calculate a few examples such as NOON states and logical qubit states for quantum error correction. In particular, our approach enables one to construct bosonic qubit error-correction codes against amplitude damping (photon loss) with a typical suppression of $\sqrt{n}-1$ losses and spanned by two logical codewords that each correspond to an $n$-photon superposition for two bosonic modes.