Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce the \textit{Latent Entropy} (L-entropy) as a novel measure to characterize the genuine multipartite entanglement in quantum systems. Our measure leverages the upper bound of reflected entropy and its maximal values attained by 2-uniform states for $n$-party ($n= 4,5$) and GHZ state for 3-party quantum systems. We demonstrate that the measure is a non-negative, local unitary invariant function which vanishes for separable states. We then analyze its interesting characteristics in spin chain models and the Sachdev-Ye-Kitaev (SYK) model. Subsequently, we explore its implications to holography by deriving a Page-like curve for the L-entropy in the CFT dual to a multi-boundary wormhole model. Furthermore, we examine the behavior of L-entropy in Haar random states, deriving analytical expressions and validating them against numerical results. In particular, we show that for $n =5$, random states approximate 2-uniform states with maximal multipartite entanglement. Furthermore, we propose a potential connection between random states and multi-boundary wormhole geometries. Extending to finite-temperature systems, we introduce the Multipartite Thermal Pure Quantum (MTPQ) state, a multipartite generalization of the thermal pure quantum state, and explore its entanglement properties. By incorporating state-dependent construction of the MTPQ state, we resolve the factorization issue in the random average of the MTPQ state, ensuring consistency with the correlation functions in the holographic dual multiboundary wormhole. Finally, we apply this construction to the multi-copy SYK model and examine its multipartite entanglement structure.
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Multipartite entanglement quantities in holographic Weyl semimetals develop features at the topological critical point and distinguish phases through anisotropic large-l scaling.
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 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.
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.
citing papers explorer
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Large $N$ factorization of families of tensor trace-invariants
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random 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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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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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.
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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.