A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries but not on RT-boundary geodesics.
Entanglement of purification: from spin chains to holography
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abstract
Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.
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hep-th 5representative citing papers
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.
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.
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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Phase transitions and uberholography of holographic pure-state geometries
A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries but not on RT-boundary geodesics.
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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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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.
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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.