Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters

Abstract

A potential quantum internet would open up the possibility of realizing numerous new applications, including provably secure communication. Since losses of photons limit long-distance, direct quantum communication and widespread quantum networks, quantum repeaters are needed. The so-called PLOBrepeaterless bound [Pirandola et al., Nat. Commun. 8, 15043 (2017)] is a fundamental limit on the quantum capacity of direct quantum communication.Here, we analytically derive the quantum-repeater gain for error-corrected, one-way quantum repeaters based on higher-dimensional qudits for two different physical encodings: Fock and multimode qudits. We identify parameter regimes in which such quantum repeaters can surpass the PLOB-repeaterless bound and systematically analyze how typical parameters manifest themselves in the quantum-repeater gain. This benchmarking provides a guideline for the implementation of error-corrected qudit repeaters.Daniel Miller: daniel.miller@hhu.de arXiv:1906.05172v1 [quant-ph]

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

“…Nonetheless, there exists a capacity limit for direct communication between two parties, the so-called PLOB-repeaterless bound [37]. However, a recent work by D. Miller [38] shows how the PLOB bound can be surpassed using error-corrected qudit repeaters, by analyzing different parameter regimes.…”

Error-corrected quantum repeaters with GKP qudits

“…After propagating a distance of L 0 , a BM combines the forward-moving qudit with the stationary qudit of the subsequent repeater station. (c) The one-way half-teleportation protocol is a GKP-adaptation of a previously-studied discrete-variable protocol [53]. Here, we add measurements to convert displacement errors into Pauli errors.…”

“…Our investigation also includes cases where the GKP code is concatenated with a higher-level QECC. Here, we focus on quantum polynomial codes that previously have been considered in combination with multi-mode and Fock-encoded qudits [50][51][52][53]. For GKP-encoded states, similar performance studies have only been carried out in the special case of qubits [54][55][56].…”