Mateusz Stępniak | Searcharxiv

arXiv2024

Local certification of unitary operations

In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.

quant-ph↗

arXiv2022

Analysis of Multiple Overlapping Paths algorithms for Secure Key Exchange in Large-Scale Quantum Networks

Quantum networks open the way to an unprecedented level of communication security. However, due to physical limitations on the distances of quantum links, current implementations of quantum networks are unavoidably equipped with trusted nodes. As a consequence, the quantum key distribution can be performed only on the links. Due to this, some new authentication and key exchange schemes must be considered to fully benefit from the unconditional security of links. One such approach uses Multiple Non-Overlapping Paths (MNOPs) for key exchange to mitigate the risk of an attack on a trusted node. The scope of the article is to perform a security analysis of this scheme for the case of both uncorrelated attacks and correlated attacks with finite resources. Furthermore, our analysis is extended to the case of Multiple Overlapping Paths (MOPs). We prove that introducing overlapping paths allows one to increase the security of the protocol, compared to the non-overlapping case with the same number of additional links added. This result may find application in optimising architectures of large-scale (hybrid) quantum networks.

quant-ph↗