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arXiv · 2512.23005

Graph restricted tensors: building blocks for holographic networks

Rafaĺ Bistroń·Márton Mestyán·Balázs Pozsgay·Karol Życzkowski
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Abstract

We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this problem by encoding these constraints in a graph is advocated; the resulting objects are called ``graph-restricted tensors''. This framework encompasses several examples previously treated in the literature, such as 1-uniform multipartite states, quantum states related to dual unitary operators and absolutely maximally entangled states (AME) corresponding to 2-unitary matrices. Original examples of presented graph-restricted tensors are motivated by tensor network models for the holographic principle. In concrete cases we find exact analytic solutions, demonstrating thereby that there exists a vast landscape of non-stabilizer tensors useful for the lattice models of holography.

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Rafaĺ Bistroń, Márton Mestyán, Balázs Pozsgay, Karol Życzkowski. 2025-12-28. Graph restricted tensors: building blocks for holographic networks. https://arxiv.org/abs/2512.23005

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