2025/06/30 by H. Miao, Ion Nechita, Hu, Miao +1
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics and Entropy #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2506.23894
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The max-flow min-cut theorem has been recently used in the theory of random tensor networks in quantum information theory, where it is helpful for computing the behavior of important physical quantities, such as the entanglement entropy. In this paper, we extend the max-flow min-cut theorem to a relation among different partial orders on the set of vertices of a network and introduce a new partial order for the vertices based on the min-cut structure of the network. We apply the extended max-flow min-cut theorem to random tensor networks and find that the finite correction to the entanglement Rényi entropy arising from the degeneracy of the min-cuts is given by the number of order morphisms from the min-cut partial order to the partial order induced by non-crossing partitions on the symmetric group. Moreover, we show that the number of order morphisms corresponds to moments of a graph-dependent measure which generalizes the free Bessel law in some special cases in free probability theory.