TY - GEN
T1 - Distance-Independent Entanglement Generation in a Quantum Network using Space-Time Multiplexed Greenberger-Horne-Zeilinger (GHZ) Measurements
AU - Patil, Ashlesha
AU - Jacobson, Joshua I.
AU - Van Milligen, Emily
AU - Towsley, Don
AU - Guha, Saikat
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - 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 super-critical 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 super-critical region expands. For a given (p,q), the entanglement rate initially increases with k, and once inside the super-critical region for a high enough k, it decays as 1/k GHZ states per time slot. When memory coherence time exponentially distributed with mean μ is incorporated, it is seen that increasing k does not indefinitely increase the super-critical region; it has a hard μ-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.
AB - 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 super-critical 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 super-critical region expands. For a given (p,q), the entanglement rate initially increases with k, and once inside the super-critical region for a high enough k, it decays as 1/k GHZ states per time slot. When memory coherence time exponentially distributed with mean μ is incorporated, it is seen that increasing k does not indefinitely increase the super-critical region; it has a hard μ-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.
KW - GHZ projections
KW - Quantum networks
KW - entanglement routing
KW - percolation
KW - time-multiplexing
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U2 - 10.1109/QCE52317.2021.00050
DO - 10.1109/QCE52317.2021.00050
M3 - Conference contribution
AN - SCOPUS:85123200646
T3 - Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
SP - 334
EP - 345
BT - Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
A2 - Muller, Hausi A.
A2 - Byrd, Greg
A2 - Culhane, Candace
A2 - Humble, Travis
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021
Y2 - 17 October 2021 through 22 October 2021
ER -