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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.
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Entanglement generation in a quantum network at distance-independent rate
Abstract We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to usen-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fusensuccessfully entangledlinks, i.e., two-qubit entangled Bell pairs shared acrossnnetwork edges, incident at that node. Implementingn-fusion, forn ≥ 3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find—by developing a connection to a modified version of the site-bond percolation problem—that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties.
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- Award ID(s):
- 1955744
- PAR ID:
- 10381750
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Quantum Information
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2056-6387
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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