Asymptotic Limits of Entanglement Transmission

Abstract:Reliable distribution of quantum entanglement over long distances is a central challenge in quantum information science, fundamentally limited by decoherence in noisy communication channels. In this work, we investigate the asymptotic limits of entanglement distribution across homogeneous linear repeater chains with arbitrary intermediate LOCC processing. We establish a strict dichotomy: the asymptotic preservation of entanglement over arbitrarily long distances is possible if and only if the underlying quantum channel admits a correctable subspace. For channels lacking such a subspace, we prove that the transmitted state converges exponentially fast to the set of separable states, rendering standard LOCC filtering insufficient. To counteract this exponential degradation, we analyze ``networks'' employing parallel channel uses per link. We derive a fundamental lower bound on the required number of parallel channel uses per elementary link, proving that for broad classes of channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement. This provides a code-independent bound for the number of physical links for the considered homogeneous one-way architecture. For depolarizing noise below the corresponding coding threshold, the logarithmic lower bound is achievable.

arXiv:2605.23443 [quant-ph]

(or arXiv:2605.23443v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.23443 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.