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More on genuine multi-entropy and holography
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More on genuine multi-entropy and holography
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By generalizing the construction of genuine multi-entropy ${\rm GM}[\mathtt{q}]$ for genuine multi-partite entanglement proposed in the previous paper arXiv:2502.07995, we give a prescription on how to construct ${\rm GM}[\mathtt{q}]$ systematically for any $\mathtt{q}$. The crucial point is that our construction naturally fits to the partition number $p(\mathtt{a})$ of integer $\mathtt{a}$. For general $\mathtt{q}$, ${\rm GM}[\mathtt{q}]$ contains $N (\mathtt{q}) = p(\mathtt{q})-p(\mathtt{q}-1)-1$ number of free parameters. Furthermore, these give $N (\mathtt{q})+1$ number of new diagnostics for genuine $\mathtt{q}$-partite entanglement. Especially for $\mathtt{q}=4$ case, this reproduces not only the known diagnostics pointed out by arXiv:1406.2663, but also a new diagnostics for quadripartite entanglement. We also study these ${\rm GM}[\mathtt{q}]$ for $\mathtt{q} = 4, 5$ in holography and show that these are of the order of ${\cal{O}}\left(1/G_N \right)$ both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.
Forward citations
Cited by 12 Pith papers
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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.
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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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Operational meaning of Markov gap in tripartite entanglement of quantum dynamics
Irreducible tripartite entanglement in free-fermion chains saturates on a slow t~L^2 timescale and its Markov gap value tracks the number of 'essential tripartite fermions' defined via a null matrix.
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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.
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Detecting Topological Transitions and Anisotropy through Multipartite Entanglement in Holographic Weyl Semimetals
Multipartite entanglement quantities in holographic Weyl semimetals develop features at the topological critical point and distinguish phases through anisotropic large-l scaling.
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Constraints on four-party entanglement in holography
In time-reflection-symmetric holographic states, I3 is necessary for non-vanishing four-party entanglement signals, bounds multi-entropy measures, and implies vanishing of Q4.
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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.
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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 tripa...
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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 g...
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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.
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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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