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Constructible reality condition of pseudo entropy via pseudo-Hermiticity

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arxiv 2209.07308 v3 pith:ORMROW6N submitted 2022-09-15 hep-th cond-mat.str-elquant-ph

Wu-zhong Guo , Song He , Yu-Xuan Zhang This is my paper · ORCID
classification hep-thcond-mat.str-elquant-ph
keywords entropypseudotransitionrealconditionmatrixquantumreality
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As a generalization of entanglement entropy, pseudo entropy is not always real. The real-valued pseudo entropy has promising applications in holography and quantum phase transition. We apply the notion of pseudo-Hermticity to formulate the reality condition of pseudo entropy. We find the general form of the transition matrix for which the eigenvalues of the reduced transition matrix possess real or complex pairs of eigenvalues. Further, we construct a class of transition matrices for which the pseudo (R\'enyi) entropies are non-negative. Some known examples which give real pseudo entropy in quantum field theories can be explained in our framework. Our results offer a novel method to generate the transition matrix with real pseudo entropy. Finally, we show the reality condition for pseudo entropy is related to the Tomita-Takesaki modular theory for quantum field theory.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Imaginary pseudo entropy encodes temporal orientation

    quant-ph 2026-06 unverdicted novelty 7.0 of 10

    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.

  2. Entanglement first law for timelike entanglement entropy and linearized Einstein's equation

    hep-th 2025-11 conditional novelty 6.0 of 10

    For timelike boundary regions, the entanglement first law ΔS = Δ⟨H⟩ is equivalent, by the paper's proof, to the linearized Einstein equations around AdS.

  3. Renormalized pseudoentropy in dS/CFT

    hep-th 2026-02 conditional novelty 5.0 of 10

    Renormalized holographic pseudoentropy in dS/CFT is constructed from conformal-gravity actions in four and six dimensions, yielding finite sphere values and Mezei-like shape dependence for small deformations.

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