A hybrid quantum repeater for qudits

TL;DR

This paper proposes a hybrid quantum repeater protocol for distributing entangled states of qudits over long distances, utilizing both discrete and continuous variables, and demonstrates its effectiveness for high-dimensional systems like qutrits.

Contribution

It introduces a novel hybrid approach combining discrete and continuous variables for long-distance entanglement distribution of qudits, including detailed analysis and achievable rates.

Findings

Qutrit entanglement surpasses qubit entanglement over lossy channels.

High-fidelity entangled qudit pairs can be distributed over 1280 km.

Three rounds of purification yield near-unit fidelity at 100 Hz rate.

Abstract

We present a "hybrid quantum repeater" protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable $d$-level systems, each of, in principle, arbitrary dimension $d$, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially (but not restricted to) efficient continuous-variable homodyne detections ("hybrid" here refers to the simultaneous exploitation of discrete and continuous variable degrees of freedom for the local processing and storage of entangled states as well as their non-local distribution, respectively). For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. With three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at rates of the order of, in principle, 100 Hz.