Distance-Independent Entanglement Generation in a Quantum Network using Space-Time Multiplexed Greenberger-Horne-Zeilinger (GHZ) Measurements
arXiv:2108.09352 · doi:10.1109/QCE52317.2021.00050
Abstract
In a quantum network that successfully creates links, shared Bell states between neighboring repeater nodes, with probability in each time slot, and performs Bell State Measurements at nodes with success probability , 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 , the rate does not change with distance in a certain 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 , the number of time slots over which a repeater can mix-and-match successful links to perform fusion on. As increases, the supercritical region expands. For a given , the entanglement rate initially increases with , and once inside the supercritical region for a high enough , it decays as GHZ states per time slot. When memory coherence time exponentially distributed with mean is incorporated, it is seen that increasing does not indefinitely increase the supercritical region; it has a hard dependent limit. Finally, we find that incorporating space-division multiplexing, i.e., running the above protocol independently in up to disconnected network regions, where 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 increases, one can approach the ultimate min-cut entanglement generation capacity of GHZ states per slot.
13 pages, q0 figures, Accepted in IEEE QCE 2021