Vaisakh Mannalath

The performance of quantum key distribution (QKD) heavily depends on statistical inference. For a broad class of protocols, the central statistical task is a random sampling problem, customarily addressed using exponential tail bounds on the hypergeometric distribution. Here, we provide an alternative solution for this task of unprecedented tightness among QKD security analyses. As a by-product, confidence intervals for the average of non-identical Bernoulli parameters follow too. These naturally fit in statistical analyses of decoy-state QKD and also outperform standard tools. Lastly, we show that, in a vast parameter regime, the use of tail bounds is not enforced because the cumulative mass function of the hypergeometric distribution is accurately computable. This sharply decreases the minimum block sizes necessary for QKD, and reveals the tightness of our simple analytical bounds when moderate-to-large blocks are considered. Mannalath, V., Zapatero, V., & Curty, M. (2024). Sharp finite statistics for quantum key distribution. arXiv:2410.04095 (2024). Currently under consideration in Phys. Rev. Lett. (second round of revision).

We propose an all-photonic protocol for distributing multipartite entangled states in quantum networks, extending the two-party quantum repeater scheme of Azuma et al. (2015) to the multipartite regime. By introducing a minimal change to the measurement pattern at user nodes, our method achieves GHZ state distribution among multiple users without the need for quantum memories.This approach maintains the core structure of the original protocol, demonstrating that scalable, memory-free entanglement distribution is achievable using only photonic resources and measurement-based operations.

Quantum Key Distribution (QKD) is a crucial technology for secure communication, relying on the principles of quantum mechanics. The security of QKD protocols is often analyzed by bounding the probability of a "failure" during the parameter estimation step. This failure probability is typically addressed using tail bounds on the hypergeometric distribution. However, existing methods can sometimes be conservative, leading to inefficiencies. In this work, we present an alternative approach that provides a more refined bound by exploiting a simple yet effective link between hypergeometric and binomial random variables.