Measurement-Device-Independent Quantum Key Distribution With Ensemble-Based Memories

Abstract

Quantum memories are enabling devices for extending the reach of quantum key distribution (QKD) systems. The required specifications for memories are, however, often considered too demanding for available technologies. One can change this mindset by introducing memory-assisted measurement-deviceindependent QKD (MDI-QKD), which imposes less stringent conditions on the memory modules. It has been shown that, in the case of fast single-qubit memories, we can reach rates and distances not attainable by single no-memory QKD links. Single-qubit memories, such as single atoms or ions, have, currently, too slow of an access time to offer an advantage in practice. Here, we relax that assumption, and consider ensemble-based memories, which satisfy the main two requirements of having short access times and large storage-bandwidth products. Our results, however, suggest that the multiple-excitation effects in such memories can be so detrimental that they may wash away the scaling improvement offered by memory-equipped systems. We then propose an alternative setup that can in principle remedy the problem. As a prelude to our main problem, we also obtain secret key generation rates for MDI-QKD systems that rely on imperfect single-photon sources with nonzero probabilities of emitting two photons.Index Terms-Quantum cryptography, measurement-deviceindependent quantum key distribution, quantum memories.

Memory-assisted quantum key distribution resilient against multiple-excitation effects

“…These requirements may be achieved by quantum memories based on atomic ensembles [11], with the added benefit of strong light-matter coupling offering the possibility for efficient implementations. Ensemble-based quantum memories may, however, allow for storage of multiple excitations [14], which have been shown to be deleterious to their performance [15]. Here, we propose two MA-MDI-QKD schemes, both relying on single-photon sources, in an attempt to rectify the multiple-excitation problem.…”

“…One of the first investigations [15] of the above technique utilized atomic-ensemble based quantum memories in conjunction with a heralding scheme based on off-resonant Raman interactions [4]. By using such a scheme [4] for interaction between weak pump signals and atomic ensembles, one can generate states with dominant terms in the form (neglecting normalization factors throughout this section) ñ ñ + ñ ñ | | | | p 0 0 1 1…”

“…Using two of such states, see figure 1(b), plus post-selection succeeding with a probability proportional to p c , one can then end up with an entangled state between two ensembles A 1 and A 2 , and their corresponding photonic modes P 1 2 , provided that p c , the excitation probability, is much lower than one. The setup in figure 1(b) was investigated in [15] and it turned out that primarily the ñ ñ ñ ñ | | | | 1 1 1 1 P A P A Figure 1. MA-MDI-QKD schemes with (a) heralding and (b) non-heralding quantum memories (QM boxes).…”

“…While it is shown that the required cavity cooperativity is not necessarily high, their entangling protocol requires an appropriate single-photon source to entangle a photon with the electron spin of the NV center [17], a combination of which has yet to be demonstrated. Another remedy to TEQM, proposed in [15], is to use nearly ideal entangled-photon (EPR) sources for creating the initial memory-photon entanglement; see figure 1(c). The idea is that if one has an EPR source that ideally generates only one pair of photons per trigger, one of these photons can be used for the side-BSM operation, whereas the other can be stored (efficiently) in the quantum memory.…”

“…Now, the latter photon can, in principle, drive only one transition and that would mitigate the multiple-excitation issue. In [15], the authors show that conventional EPR sources relying on parametric downconversion would not solve the problem, but suggest to instead use quantum-dot based EPR sources, which have been shown to have very low second-order coherence properties [19]. Similarly, this solution would benefit quantum repeater implementations [20].…”