@article{11ed36f852ea4a2f8cf789e0ab0aa7cd,
title = "Quantum Max-flow in the Bridge Graph",
abstract = "The quantum max-flow is a linear algebraic version of the classical max-flow of a graph, used in quantum many-body physics to quantify the maximal possible entanglement between two regions of a tensor network state. In this work, we calculate the quantum max-flow exactly in the case of the bridge graph. The result is achieved by drawing connections to the theory of prehomogenous tensor spaces and the representation theory of quivers. Further, we highlight relations to invariant theory and to algebraic statistics.",
keywords = "(primary) 15A69, (secondary) 81P42, 14L24, 16G20, Castling transform, Entanglement, Quantum max-flow, Tensor network",
author = "Fulvio Gesmundo and Vladimir Lysikov and Vincent Steffan",
note = "Funding Information: F.G.\u2019s work is partially supported by the Thematic Research Programme \u201CTensors: geometry, complexity and quantum entanglement\u201D, University of Warsaw, Excellence Initiative \u2013 Research University and the Simons Foundation Award No. 663281 granted to the Institute of Mathematics of the Polish Academy of Sciences for the years 2021\u20132023. We thank Mathias Drton, Alexandros Grosdos, Visu Makam and Philipp Reichenbach for helpful discussions and for pointing out the connections to algebraic statistics and to the representation theory of quivers. This work was done while V.L. was at the University of Copenhagen. V.L. and V.S. acknowledge financial support from the European Research Council (ERC Grant Agreement No. 818761), VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). V.S. thanks Matthias Christandl and Frederik Ravn Klausen for helpful discussions and Or Sattath for proposing the problem. Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",
year = "2024",
doi = "10.1007/s00031-024-09863-2",
language = "English",
journal = "Transformation Groups",
issn = "1083-4362",
publisher = "Springer Basel AG",
}