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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Fun with replicas: tripartitions in tensor networks and gravity
16 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We introduce a new correlation measure for tripartite pure states that we call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$, $B$, $C$, invariant under local unitaries, and is bounded from above by $\log d_A d_B$. For random tensor network states, we prove that $G(A:B:C)$ is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with $A$, $B$, and $C$. We argue that for holographic states with a fixed spatial geometry, $G(A:B:C)$ is similarly computed by the minimal area tripartition. For general holographic states, $G(A:B:C)$ is determined by the minimal area tripartition in a backreacted geometry, but a smoothed version is equal to the minimal tripartition in an unbackreacted geometry at leading order. We briefly discuss a natural family of quantities $G_n(A:B:C)$ for integer $n \geq 2$ that generalize $G=G_2$. In holography, the computation of $G_n(A:B:C)$ for $n>2$ spontaneously breaks part of a $\mathbb{Z}_n \times \mathbb{Z}_n$ replica symmetry. This prevents any naive application of the Lewkowycz-Maldacena trick in a hypothetical analytic continuation to $n=1$.
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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.
Genuine multi-entropy in the toric code reduces to topological entanglement entropy for stabilizer states at low replica index but captures independent topological data at n=4 and for non-stabilizer states.
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
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.
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
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.
citing papers explorer
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Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant
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.
-
Multi-entropy in random tensor networks
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.
-
Structural Obstruction to Replica Symmetry Breaking for Multi-Entropy in Random Tensor Networks
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.
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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.
-
Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
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.
-
Genuine Multi-Entropy in the Toric Code
Genuine multi-entropy in the toric code reduces to topological entanglement entropy for stabilizer states at low replica index but captures independent topological data at n=4 and for non-stabilizer states.
-
Subregion observer rules from generalized entanglement wedges
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
-
Universal entanglement probes of topological order and locally-achiral manifolds
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.
-
Genuine multientropy, dihedral invariants and Lifshitz theory
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.
-
The Entanglement Wedge Polygon
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
-
Multi-entropy in heavy local quenches
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.
-
Constraints on four-party entanglement in holography
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.
-
Properties of tensorial free cumulants
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 in Confining Holographic Backgrounds
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.
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Tripartite Correlation Signal from Multipartite Entanglement of Purification
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.
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Rethinking quantum information in gravity and fields
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.