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.
On the real-time evo- lution of pseudo-entropy in 2d CFTs,
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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.
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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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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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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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.