Simple Efficient Decoders for Quantum Key Distribution Over Quantum Repeaters with Encoding

Abstract

We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we propose two decoder structures for encoded repeaters that not only improve system performance but also make the implementation aspects easier by removing two-qubit gates from the QKD decoder. By developing several scalable numerical and analytical techniques, we then identify the resilience of the setup to various sources of error in gates, measurement modules, and initialization of the setup. We apply our techniques to three-and fivequbit repetition codes and obtain the normalized secret key generation rate per memory per second for encoded and probabilistic quantum repeaters. We quantify the regimes of operation, where one class of repeater outperforms the other, and find that there are feasible regimes of operation where encoded repeaters-based on simple three-qubit repetition codes-could offer practical advantages.

Quantum repeaters with encoding on nitrogen-vacancy center platforms

“…Note that the remote cnot circuit in Fig. 1 is slightly different from the one used in [13,14]. In the latter work, the remote cnot circuit requires measurements on nuclear spins.…”

“…Moreover, such memories are adopted for the first demonstration of a simple QR network between four cities in Netherlands [11,12]. This offers a promising platform for the implementation of near-future encoded QR structures, as our recent work on QRs with encoding [13,14] suggests that the simple three-qubit repetition code could be the best option for quantum key distribution (QKD) applications over short to moderately long distances. In particular, we find that there are working regimes of operation where encoded QRs can outperform probabilistic QRs [14].…”

“…This offers a promising platform for the implementation of near-future encoded QR structures, as our recent work on QRs with encoding [13,14] suggests that the simple three-qubit repetition code could be the best option for quantum key distribution (QKD) applications over short to moderately long distances. In particular, we find that there are working regimes of operation where encoded QRs can outperform probabilistic QRs [14]. This means that for the type of networks that we are expecting to have in short term, it could be a rewarding exercise to implement encoded QRs despite their additional implementation challenges.…”

“…To get an accurate view of the requirements, versus gains, for NV-center based QRs with encoding, we need to consider realistic scenarios that such memories can be used in. While, in earlier works by our group [13,14], the performance of the QRs with three-qubit repetition codes is carefully studied in the presence of operational errors, such analyses are not directly applicable to the case of NV centers. Firstly, the work in [13,14] assumes that a direct deterministic Bell-state measurement (BSM) on two separate QMs is readily available.…”

“…While it is possible to use an entangled link between the electron spins of two NV centers to mediate a joint operation on them [15], we should account for additional errors, or delays, that this may cause, and also different QR structures that we can then come up with based on this mediatory entangled link. Secondly, the work in [13,14] ignores the impact of memory decoherence. Now that we have a chosen memory, which is short of ideal once it gets to coherence times, we should consider its effect on the performance to have a better assessment of system requirements.…”