Memory-assisted quantum key distribution with a single nitrogen-vacancy center

Memory-assisted measurement-device-independent quantum key distribution (MA-MDI-QKD) is a promising scheme that aims to improve the rate-versus-distance behavior of a QKD system by using the state-of-the-art devices. It can be seen as a bridge between current QKD links to quantum repeater based networks. While, similar to quantum repeaters, MA-MDI-QKD relies on quantum memory (QM) units, the requirements for such QMs are less demanding than that of probabilistic quantum repeaters. Here we present a variant of MA-MDI-QKD structure that relies on only a single physical QM: a nitrogen-vacancy center embedded into a cavity where its electronic spin interacts with photons and its nuclear spin is used for storage. This enables us to propose a simple but efficient MA-MDI-QKD scheme resilient to memory errors and capable of beating, in terms of rate and reach, existing QKD demonstrations. We also show how we can extend this setup to a quantum repeater system, reaching, thus, larger distances.

Figure 1

MA-MDI-QKD with (a) two nonheralding physical memories, (b) a single memory with two qubits, and (c) its extension to a three-leg quantum repeater system.

Figure 2

The double-encoding module proposed in [9]. It allows us to entangle a polarized photon with an NV center in a cavity. This module will be used for transferring users' states into the electron spin of the NV center.

Figure 3

Schematic diagram for the sequential operations in the protocol on each of the nuclear ($n$) and electron ($e$) spins. The subscript A (B) refers to the interaction of the electron spin with Alice (Bob) photon. The detailed description of each step and its required operations is given in Appendix pp2.

Figure 4

Secret key generation rates versus distance for our proposed single-memory MDI-QKD scheme and its comparison with a no-QM system (PLOB) driven at 100 MHz (lower curve) and 1 GHz (upper curve) as well as the two-QM setup proposed in [9]. In the latter case, the coherence time of the electron spin $T_e$ ranges from 30 to 100 ms. $T_n$ refers to the coherence time of the nuclear spin, which is the relevant time constant for the setup proposed here.

Figure 5

Secret key generation rates versus distance for our proposed single-memory MDI-QKD scheme and its comparison with no-QM MDI-QKD driven at 1 GHz for different values of error probabilities associated with the logic gates of Fig. 3.

Figure 6

Secret key generation rates versus distance for the quantum repeater setup of Fig. 1 and our proposed single-memory MDI-QKD scheme at $T_n=1$ s.