Constructible reality condition of pseudo entropy via pseudo-Hermiticity

Abstract

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 (Rényi) 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.

13+18 pages; v2: Minor changes, typos corrected and references added; v3: Added a new proposition (proposition 1) and modified the example in 2d free scalar. Match the published version

References in corpus (13)

• Making Sense of Non-Hermitian Hamiltonians
• Non-Hermitian Physics
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Pseudo Entropy in Free Quantum Field Theories
• Aspects of Pseudo Entropy in Field Theories
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Topological pseudo entropy
• On the Page curve under final state projection
• Subregion Spectrum Form Factor via Pseudo Entropy
• On the real-time evolution of pseudo-entropy in 2d CFTs
• Pseudo complexity of purification for free scalar field theories
• Pseudo Entropy in $U(1)$ gauge theory
• Twist operators and pseudo entropies in two-dimensional momentum space

Cited by in corpus (14)

• Time-like Entanglement Entropy in AdS/BCFT
• SVD Entanglement Entropy
• Entanglement Phase Transition in Holographic Pseudo Entropy
• Pseudo entropy under joining local quenches
• Holographic Timelike Entanglement Entropy from Rindler Method
• Relation between time- and spacelike entanglement entropy
• Sum rule for the pseudo-Rényi entropy
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Complex entanglement entropy for complex conformal field theory
• Symmetry Properties of Quantum Dynamical Entropy
• Detecting quantum chaos via pseudo-entropy
• Holographic timelike entanglement and $c$ theorem for supersymmetric QFTs in ($0+1$)d
• Spectral Projections for Density Matrices in Quantum Field Theories