Entanglement capacity of complex networks from quantum walks

Abstract

Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic protocols. However, this notion relies on a fixed Hilbert space factorization separating coin and position and is therefore not directly applicable to more complex, irregular structures. Here we introduce an entanglement measure for general networks based on a bipartition that assigns each node two roles, acting as both a source and a target. The resulting bipartition defines the source-target entanglement, a measure for general networks, motivated by coin-walker entanglement. We show that the connectivity of the network imposes an upper bound on this entanglement and identify graph matchings as the underlying structure governing entanglement generation. We further illustrate that in random graphs improving graph connectivity reduces the attainable entanglement, establishing a structure-dependent constraint on quantum correlations.