  Quantum communication networks are crucial for both secure communication and
cryptographic networked tasks. Building quantum communication networks in a
scalable and cost-effective way is essential for their widespread adoption,
among which a stable and miniaturized high-quality quantum light source is a
key component. Here, we establish a complete polarization entanglement-based
fully connected network, which features an ultrabright integrated Bragg
reflection waveguide quantum source, managed by an untrusted service provider,
and a streamlined polarization analysis module, which requires only one
single-photon detector for each end user. We perform a continuously working
quantum entanglement distribution and create correlated bit strings between
users. Within the framework of one-time universal hashing, we provide the first
experimental implementation of source-independent quantum digital signatures
using imperfect keys circumventing the necessity for private amplification.
More importantly, we further beat the 1/3 fault-tolerance bound in Byzantine
agreement, achieving unconditional security without relying on sophisticated
techniques. Our results offer an affordable and practical route for addressing
consensus challenges within the emerging quantum network landscape.
