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.
hub
New multipartite entanglement measure and its holographic dual
16 Pith papers cite this work. Polarity classification is still indexing.
16
Pith papers citing it
abstract
In this letter we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate "soap-film" anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the sub-leading corrections in G_N.
hub tools
citation-role summary
background 3
method 1
citation-polarity summary
representative citing papers
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.
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
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.
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.
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.
Generalizes the holographic signal inequality to mixed states, finds violations due to vanishing Markov gap in some geometries, restores it on canonical purification, and conjectures a new inequality.
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.
Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.
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
-
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.
-
Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
-
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.
-
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.
-
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.
-
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.
-
On a mixed-state extension of the holographic signal inequality
Generalizes the holographic signal inequality to mixed states, finds violations due to vanishing Markov gap in some geometries, restores it on canonical purification, and conjectures a new inequality.
-
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.
-
Separability from Multipartite Measures
Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.
-
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.
-
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.
-
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.