Distance-Independent Entanglement Generation in a Quantum Network using Space-Time Multiplexed Greenberger-Horne-Zeilinger (GHZ) Measurements

TL;DR

This paper introduces a distance-independent entanglement generation protocol in quantum networks using space-time multiplexed GHZ measurements, expanding the supercritical region and improving rates through multiplexing and network division.

Contribution

It extends GHZ-based entanglement protocols with space-time multiplexing and network division, achieving near-capacity rates and distance independence in quantum network entanglement generation.

Findings

Distance-independent entanglement rate in certain parameter regions.

Supercritical region expands with multiplexing blocklength $k$.

Approaching the network's min-cut capacity with increased multiplexing.

Abstract

In a quantum network that successfully creates links, shared Bell states between neighboring repeater nodes, with probability $p$ in each time slot, and performs Bell State Measurements at nodes with success probability $q<1$, the end to end entanglement generation rate drops exponentially with the distance between consumers, despite multi-path routing. If repeaters can perform multi-qubit projective measurements in the GHZ basis that succeed with probability $q$, the rate does not change with distance in a certain $(p,q)$ region, but decays exponentially outside. This region where the distance independent rate occurs is the supercritical region of a new percolation problem. We extend this GHZ protocol to incorporate a time-multiplexing blocklength $k$, the number of time slots over which a repeater can mix-and-match successful links to perform fusion on. As $k$ increases, the supercritical region expands. For a given $(p,q)$, the entanglement rate initially increases with $k$, and once inside the supercritical region for a high enough $k$, it decays as $1/k$ GHZ states per time slot. When memory coherence time exponentially distributed with mean $\mu$ is incorporated, it is seen that increasing $k$ does not indefinitely increase the supercritical region; it has a hard $\mu$ dependent limit. Finally, we find that incorporating space-division multiplexing, i.e., running the above protocol independently in up to $d$ disconnected network regions, where $d$ is the network's node degree, one can go beyond the 1 GHZ state per time slot rate that the above randomized local link-state protocol cannot surpass. As $(p,q)$ increases, one can approach the ultimate min-cut entanglement generation capacity of $d$ GHZ states per slot.