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 wide-spread quantum networks, quantum repeaters are needed. The so-called PLOB-repeaterless 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.
Highlights
The prospect of an eventual world-spanning quantum internet motivates tremendous interest and investments [1,2,3]
As the quantum capacity is closely related to the amount of transmissible quantum information, direct transmission channels are not well suited for long distance quantum connections
Quantum repeaters have been proposed [15,16,17,18,19,20]. They shorten the distance of direct transmissions by introducing intermediate repeater stations such that losses and errors can be tackled using entanglement heralding, quantum memories, entanglement distillation, or quantum error-correcting codes (QECCs) [20]
Summary
The prospect of an eventual world-spanning quantum internet motivates tremendous interest and investments [1,2,3]. As the quantum capacity is closely related to the amount of transmissible quantum information, direct transmission channels are not well suited for long distance quantum connections To overcome these limitations, quantum repeaters have been proposed [15,16,17,18,19,20]. We use a different approach by exploiting that the quantum capacity of an error-corrected quantum repeater can be lower bounded by log2(D) − H(P ), where H(P ) is the Shannon entropy of the error probability distribution P of the state distributed by the repeater [14, 42]. We identify and discuss parameter regimes in which error-corrected, one-way quantum repeaters based on qudits can beat the PLOB-repeaterless bound.
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