Long-distance device-independent quantum key distribution with standard optics tools

TL;DR

This paper tackles the practical bottleneck of device-independent QKD by introducing two heralding-based protocols that use only standard quantum-optics components—two-mode squeezed states, displacement operations, and on-off detectors—to enable long-distance DI-QKD. It combines single-photon interference heralding with noisy preprocessing and analyzes the performance using Gaussian-state formalism and NPA-based SDP optimization to bound Eve’s information and compute asymptotic key rates. The results show substantial distance advantages over direct transmission, identifying an optimal mean photon number and detector-efficiency thresholds (approximately $0.858$–$0.917$) that still enable secure keys under realistic imperfections. The work emphasizes experimental feasibility and outlines extensions to finite-size security and potential local Bell-test enhancements to further ease practical requirements.

Abstract

Device-independent quantum key distribution (DI-QKD) enables information-theoretically secure key exchange between remote parties without any assumptions on the internal workings of the devices used for its implementation. However, its practical deployment remains severely constrained by the need for loophole-free Bell inequality violations, which are highly susceptible to losses and detection efficiencies. In this paper, we propose two long-distance DI-QKD protocols based on a heralding scheme using single-photon interference. Our protocols consist of only standard quantum optics tools such as two-mode squeezed states, displacement operations and on-off detectors, making them experimentally accessible. To further enhance robustness against realistic imperfections, we integrate a classical noisy preprocessing technique during post-processing. We calculate key rates of the protocols by numerical optimization and show the supremacy of this implementation over existing protocols in terms of communication distances.

Figures (7)

• Figure 1: Schematics of our DI-QKD protocols. (a) Protocol A. Alice and Bob prepare two-mode squeezed states and transmit one-mode to the central station through pure-loss channels. At the central station, these modes are interfered with a 50:50 beamsplitter and detected with on-off detectors. Alice and Bob perform displacement operations on their remaining modes followed by measurements using on-off detectors. Alice and Bob share a secret key by using events where exactly one of the two on-off detectors clicks. (b) Protocol B. Bob prepares a single-photon entanglement by using a two-mode squeezed state, a heralding detector and a beamsplitter, and sends one-mode of the entanglement to the central station. Alice and Bob share a secret key from events where only one of the two on-off detectors at the central station and the heralding detector click simultaneously.
• Figure 2: Key rate of Protocol A versus distance $L$ for different mean photon number $\bar{n}$. We take $\eta_e = \eta_d = 0.95$ and $p_d = 10^{-6}$.
• Figure 3: Key rate versus distance $L$. Blue circles, green squares and black dashed line represent key rates of Protocol A, Protocol B and the direct transmission protocol, respectively. We take $\eta_d = \eta_e = 0.95$ and $p_d = 10^{-6}$. We use $\bar{n} = 0.015$ for Protocol A, $\bar{n} = 0.01$ for Protocol B, and we optimize the mean photon number for each key rate for the direct transmission protocol.
• Figure 4: Key rate of protocol A versus distance $L$ for different detection efficiency $\eta_e$. We take $\eta_d = 0.95$ and $p_d = 10^{-6}$.
• Figure 5: Key rate of protocol B versus distance $L$ for different detection efficiency $\eta_e$. We take $\eta_d = 0.95$ and $p_d = 10^{-6}$.