Related papers: Canonical partial ordering from min-cuts and quant…

The quantum max-flow min-cut conjecture relates the rank of a tensor network to the minimum cut in the case that all tensors in the network are identical\cite{mfmc1}. This conjecture was shown to be false in Ref. \onlinecite{mfmc2} by an…

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a…

The max-flow min-cut theorem is a cornerstone result in combinatorial optimization. Calegari et al. (arXiv:0802.3208) initialized the study of quantum max-flow min-cut conjecture, which connects the rank of a tensor network and the min-cut.…

We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…

Intrigued by the capacity of random networks, we start by proving a max-flow min-cut theorem that is applicable to any random graph obeying a suitably defined independence-in-cut property. We then show that this property is satisfied by…

In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…

Large-scale quantum networks have been employed to overcome practical constraints of transmissions and storage for single entangled systems. Our goal in this article is to explore the strong entanglement distribution of quantum networks. We…

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are "orthogonal" to each other, in the sense that the flow saturates the cut and is zero…

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…

A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…

The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…

A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…

Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut theorem for boundary regions, applied recently to develop a "bit-thread" interpretation of…

A min-cut that seperates vertices s and t in a network is an edge set of minimum weight whose removal will disconnect s and t. This problem is the dual of the well known s-t max-flow problem. Several algorithms for the min-cut problem are…

We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined…

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…

We give the first almost-linear total time algorithm for deciding if a flow of cost at most $F$ still exists in a directed graph, with edge costs and capacities, undergoing decremental updates, i.e., edge deletions, capacity decreases, and…

For general random tensor network states at large bond dimension, we prove that the integer R\'enyi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal…