Performance of device-independent quantum key distribution

Quantum key distribution provides information-theoretically-secure communication. In practice, device imperfections may jeopardise the system security. Device-independent quantum key distribution solves this problem by providing secure keys even when the quantum devices are untrusted and uncharacterized. Following a recent security proof of the device-independent quantum key distribution, we improve the key rate by tightening the parameter choice in the security proof. In practice where the system is lossy, we further improve the key rate by taking into account the loss position information. From our numerical simulation, our method can outperform existing results. Meanwhile, we outline clear experimental requirements for implementing device-independent quantum key distribution. The maximal tolerable error rate is 1.6%, the minimal required transmittance is 97.3%, and the minimal required visibility is $96.8\%$.

Figure 1

CHSH game: Alice and Bob agree on a strategy before the game. During the game, they cannot communicate. Alice (Bob) is given an input bit $x$ ($y$) and is required to output a bit $a$ ($b$). Their goal is to let the outputs satisfy $a\oplus b=xy.$

Figure 2

Illustration of the protocol. Alice and Bob measure their joint states in $n$ rounds, among which a red subset is randomly selected for tests.

Figure 3

The solid line shows the value of $\tau$ corresponding to the optimized key rate. It decreases from 1 to 0.49 as $e$ increases from 0 to $1.6\%$. The dashed line shows the analytical approximation ${\tau }_{\text{opt}}$, which is very close to the numerically optimal $\tau$. The dot-dashed line stands for the value of $\tau$ in the Vazirani–Vidick proof.

Figure 4

The key rate of our optimized formula, the Vazirani–Vidick proof, the Miller–Shi proof, and the conjectured optimal key rate. For every value of noise parameter $e$, our key rate (solid line) is better than the Vazirani–Vidick proof (dashed line). The maximum allowable noise is also increased from $1.5\%$ to $1.6\%$. Comparing with the Miller–Shi proof (dot dashed line), our work also has superior performance in most parameter regions.

Figure 5

Deviation of angle. The two solid lines stand for the ideal basis direction, while the two dashed lines stand for the deviated basis direction. The angle between the two deviated basis direction is shown to be $\pi /8+2\theta$.

Figure 6

Transmittance $\eta$ vs misalignment $\theta$. As more misalignment is allowed, the required minimum detector efficiency becomes higher. Four cases are considered, basic constraint for our result, Vazirani–Vidick, Miller–Shi, and refined constraint for our result.