Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.
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For n=2, Rényi multi-entropies in RTNs are determined by minimal multiway cuts; the minimal multiway cut conjecture fails for integer n>2 with explicit counterexamples.
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
Permutation defects between wavefunction replicas yield multipartite entanglement measures that capture the chiral central charge from bulk states in chiral topological phases.
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
The paper defines the entanglement wedge polygon as the intersection of entanglement wedges external to individual homology regions and studies its topological and geometric properties in AdS examples.
Multi-entropy measures extract the topological partition function Z(M) for locally-achiral manifolds, enabling access to universal properties of 2+1d topological phases beyond S and T and detection of 4d beyond-cohomology T-SPT.
Authors derive genuine multientropy for Lifshitz states as mutual information plus negativity, obtain its non-integer Rényi continuation, and prove dihedral invariants equal Rényi reflected entropies for general tripartite pure states.
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
In time-reflection-symmetric holographic states, I3 implies vanishing of multiple four-party entanglement measures and bounds those from multi-entropy, though Q4 is not quantitatively bounded by I3.
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.
The junction law for multipartite entanglement persists in confining holographic backgrounds, but phase structure and GM short-distance scaling (L^{-4}, L^{-2}, or L^{-2}(log L)^2) are background-dependent.
Δ^(3)_p is a non-negative signal detecting genuine tripartite entanglement, extended via the E_w = E_p conjecture to holographic systems in AdS3/CFT2.
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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Probing chiral topological states with permutation defects
Permutation defects between wavefunction replicas yield multipartite entanglement measures that capture the chiral central charge from bulk states in chiral topological phases.