Towards Device-Independent Quantum Key Distribution with Photonic Devices

TL;DR

This work tackles the challenge of realizing device-independent QKD (DIQKD) in photonic hardware by combining a machine-learned optical circuit with a memory-efficient block SDP hierarchy to bound the conditional von Neumann entropy $H(A|E)$. It advances both asymptotic and finite-size security analyses by exploiting full observed statistics via an $I$-score Bell certificate and Entropy Accumulation Theorem-based reasoning, enabling significantly tighter key-rate bounds than CHSH-based approaches. The results demonstrate that the identified photonic circuit can tolerate realistic loss and noise levels and, crucially, that finite-size effects can be mitigated to achieve practical key generation within feasible experimental runtimes (e.g., ~8 hours at 1 MHz with $\eta=87.5\%$). Overall, the work shows that photonic DIQKD is within experimental reach using commercial components and provides a versatile framework applicable to other photonic DIQKD architectures and entropy-based security proofs.

Abstract

Quantum Key Distribution (QKD) protocols enable two distant parties to communicate with information-theoretically proven secrecy. However, these protocols are generally vulnerable to potential mismatches between the physical modeling and the implementation of their quantum operations, thereby opening opportunities for side channel attacks. Device-Independent (DI) QKD addresses this problem by reducing the degree of device modeling to a black-box setting. The stronger security obtained in this way comes at the cost of a reduced noise tolerance, rendering experimental demonstrations more challenging: so far, only one experiment based on trapped ions was able to successfully generate a secret key. Photonic platforms have however long been preferred for QKD thanks to their suitability to optical fiber transmission, high repetition rates, readily available hardware, and potential for circuit integration. In this work, we assess the feasibility of DIQKD on a photonic circuit recently identified by machine learning techniques. For this, we introduce an efficient converging hierarchy of semi-definite programs (SDP) to bound the conditional von Neumann entropy and develop a finite-statistics analysis that takes into account full outcome statistics. Our analysis shows that the proposed optical circuit is sufficiently resistant to noise to make an experimental realization realistic.

Figures (14)

• Figure 1: Optical setup. Two vacuum modes are entangled via a two-mode squeezer and distributed to Alice and Bob. Each party uses a local random number generator (RNG) to select measurement settings ($x$ for Alice, $y$ for Bob). Their respective modes undergo displacements parameterized by $\alpha_x$ and $\beta_y$, subsequently measured via photon detectors, yielding binary outcomes $a$ and $b$ (0: no click, 1: click).
• Figure 2: Lower bound on the asymptotic key rate as a function of the efficiency $\eta$, with a security based on the CHSH score (in red), and on the full statistics (in blue).
• Figure 3: Minimum number of run $n$ leading to a positive key rate with $\epsilon_\text{snd}=3\times 10^{-10}$ when basing the security on the CHSH score (in red), and on full statistics (in blue), as a function of the efficiency $\eta$.
• Figure 4: In the first noise model, the TMS acts on two families of optical modes, but the displacements only act on one of them.
• Figure 5: In the second noise model, the displacements act on two families of optical modes, but the TMS only acts on one of them.

Theorems & Definitions (2)

• Proposition 1
• proof