Device-independent quantum key distribution with spin-coupled cavities

Device-independent quantum key distribution (DIQKD) guarantees the security of a shared key without any assumptions on the apparatus used, provided that the observed data violates a Bell inequality. Such a violation is challenging experimentally due to photodetection inefficiencies and, especially, channel losses. Here we describe a realistic DIQKD implementation based on the interaction between light and spins stored in cavities, which allows a heralded mapping of polarization entanglement of light onto the spin. The spin state can subsequently be measured with near unit efficiency. Heralding alleviates the effect of channel loss, and as the protocol allows for local heralding, the spin decay is not affected by the communication time between the parties, making a Bell inequality violation over an arbitrary distance possible. We compute the achievable key rates for realistic parameter values and find significant improvements over entirely optical implementations in the key bits per source use and the attainable distance.

Figure 1

(a) Symmetric protocol. A source emits entangled photon pairs. Each party holds a spin in a cavity, initialized in $(|\uparrow \rangle +|\downarrow \rangle )/\sqrt{2}$. One photon interacts with each cavity and, if reflected, is measured in the $|H\rangle$,$|V\rangle$ basis. When such a heralding detection occurs on both sides, the photonic entanglement is mapped onto the spins. Upon heralding, Alice chooses a basis and reads out her spin (similarly for Bob). The spin measurement data is used for the Bell test and key generation. (b) Asymmetric protocol. Bob proceeds as above, but Alice has no cavity. Instead, she directly measures the polarization of the photon she receives. The source is located at Alice's side to minimize channel losses preceding her measurement.

Figure 2

A positive key rate can be obtained in the region under the curves for the symmetric (dotted) and the asymmetric protocol with ${\eta }_d=1.0$, 0.9, and 0.8 (solid, top to bottom). Note that beyond $\kappa /{\kappa }_s\sim 10$ increasing $\kappa /{\kappa }_s$ further does not improve the range for $t/\tau$ significantly.

Figure 3

(a) Rates of the symmetric (left) and asymmetric (right) protocols at $L=10$ km with $r=100$ MHz (contours separated by $5\times {10}^3$ bits/s). (b) Key rate in units of the repetition rate in the collective attacks (solid) and BQS (dashed) scenarios. The symmetric and asymmetric protocol rates are shown in each case (upper red and lower black curves), and $\kappa /{\kappa }_s=6$, $t/\tau =0.01$. The rate of Ref. [13] is also shown (gray dotted). For all plots ${\eta }_{\text{her}}={\eta }_d=0.855$ and $L_{\text{att}}=22$ km.

Figure 4

Key rates for the asymmetric (upper black curves) and symmetric (lower red curves) protocol. Solid lines are $R_{A,S}$ and dashed are $R_{A,S}^{\text{signal}}$. As expected, key rates with instant communication are higher (see text). Nevertheless, this difference can be neglected and, for each protocol, these two plots bound the optimal key rate achievable without communication. We took the moderate values $\kappa /{\kappa }_s\simeq 6$ and ${\eta }_d=0.855$ (for the asymmetric protocol). Increasing these values will only bring the curves closer together.