The calibrated pseudo-Rényi phase and replica visibility exactly equal the Helstrom trace distance between forward and backward ancilla states, giving a bounded operational meaning to imaginary pseudo entropy.
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PseudoentropyindS/CFT and Timelike Entanglement Entropy.Phys
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abstract
We study holographic entanglement entropy in dS/CFT and introduce time-like entanglement entropy in CFTs. Both of them take complex values in general and are related with each other via an analytical continuation. We argue that they are correctly understood as pseudo entropy. We find that the imaginary part of pseudo entropy implies an emergence of time in dS/CFT.
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Proposes stress tensor deformation dictionary in dS/CFT via metric-flow and mixed boundary conditions at future infinity, with exact consistency check in Kerr-dS3/CFT2 and pseudo entropy computations for TTbar and root-TTbar deformations.
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mechanics, random matrices, and Chern-Simons theory.
Late-time linear growth of holographic TEE is governed by an interior critical surface Ac whose existence is guaranteed by NEC under Kasner asymptotics, with vacuum maximizing real growth and minimizing imaginary part.
Boundary-CFT scaling dimensions and central charge can be reconstructed from the system-size dependence and phase of Loschmidt echoes after a critical quench, bypassing ground-state preparation.
Complexified exactly-marginal couplings produce solvable complex CFTs, with the Ising defect verified numerically in non-Hermitian chains.
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
Pseudo entropy distinguishes topological from trivial phases in the SSH model via sign of averaged excess entropy ΔS12 and tracks quench critical times with its imaginary part.
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the influence functional.
Timelike mutual information is positive and weak monotonicity holds for non-overlapping timelike subregions in AdS3-Vaidya holography, but the timelike strong subadditivity is violated for overlapping intervals while Araki-Lieb and subadditivity hold.
An operator-algebraic definition of timelike entanglement entropy in QFT is shown to be real-valued via the timelike tube theorem.
citing papers explorer
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Imaginary pseudo entropy encodes temporal orientation
The calibrated pseudo-Rényi phase and replica visibility exactly equal the Helstrom trace distance between forward and backward ancilla states, giving a bounded operational meaning to imaginary pseudo entropy.
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Stress Tensor Deformations in dS/CFT: Mixed Boundary Conditions, Spectrum Flow and Pseudo Entropy
Proposes stress tensor deformation dictionary in dS/CFT via metric-flow and mixed boundary conditions at future infinity, with exact consistency check in Kerr-dS3/CFT2 and pseudo entropy computations for TTbar and root-TTbar deformations.
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Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mechanics, random matrices, and Chern-Simons theory.
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Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents
Late-time linear growth of holographic TEE is governed by an interior critical surface Ac whose existence is guaranteed by NEC under Kasner asymptotics, with vacuum maximizing real growth and minimizing imaginary part.
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Extracting conformal data from Loschmidt echoes after critical quenches
Boundary-CFT scaling dimensions and central charge can be reconstructed from the system-size dependence and phase of Loschmidt echoes after a critical quench, bypassing ground-state preparation.
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Complex Conformal Manifolds
Complexified exactly-marginal couplings produce solvable complex CFTs, with the Ising defect verified numerically in non-Hermitian chains.
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Real-time pseudo entropy and modular-Hamiltonian correlations
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
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No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
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Pseudo entropy and topological phases of matter
Pseudo entropy distinguishes topological from trivial phases in the SSH model via sign of averaged excess entropy ΔS12 and tracks quench critical times with its imaginary part.
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Holographic complexity of de-Sitter black holes
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
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Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems
Generic ergodic Hamiltonian dynamics in quantum Ising chains exhibits a long mesoscopic regime in temporal entanglement that deviates from random-circuit universality, suggesting slow spectral reorganization of the influence functional.
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Entanglement inequalities for timelike intervals within dynamical holography
Timelike mutual information is positive and weak monotonicity holds for non-overlapping timelike subregions in AdS3-Vaidya holography, but the timelike strong subadditivity is violated for overlapping intervals while Araki-Lieb and subadditivity hold.
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Timelike entanglement entropy Revisited
An operator-algebraic definition of timelike entanglement entropy in QFT is shown to be real-valued via the timelike tube theorem.
- The Thermodynamics of Cosmological Horizons and Their Holographic Description in de Sitter Space
- Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography