arXiv subjects

Wu-zhong Guo

Publications and source records attributed to Wu-zhong Guo.

At least 19 recordsLinked to original sources

arXiv2026

Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization

We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer Rényi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer Rényi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.

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arXiv2026

Quantum information loss

We introduce a measure of information loss for any quantum process that may be modeled by a prepare-evolve-measure scenario: Alice prepares an ensemble of states that gets sent via a quantum channel to Bob, who then measures the output. As a quantum channel models open system dynamics, our measure of information loss quantifies Bob's inability to retrodict with certainty which state Alice sent through the channel. By minimizing this measure over all possible pure state ensemble decompositions of a fixed state $ρ$, and over all POVMs on the output of a channel $\mathcal{E}$, we arrive at an intrinsic notion of information loss for any state-channel pair $(ρ,\mathcal{E})$. We show that the vanishing of information loss with respect to all states supported on a fixed codespace $\mathcal{H}_{\text{code}}$ is equivalent to a condition we term \emph{universal pristineness}, which ensures that orthogonal pure states in $\mathcal{H}_{\text{code}}$ get sent via the channel $\mathcal{E}$ to possibly mixed states whose supports are orthogonal. Moreover, we prove universal pristineness is equivalent to the Knill-Laflamme conditions in quantum error correction, which are necessary and sufficient for the existence of a perfect recovery channel for all states supported on $\mathcal{H}_{\text{code}}$. As an application, we apply our framework to the Hayden-Preskill model of black hole evaporation, demonstrating that the evaporation channel becomes asymptotically universally pristine, thereby providing a purely channel-theoretic formulation of Page-time information retrieval.

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arXiv2026

Selecting Complex Extremal Surfaces with the Kontsevich--Segal--Witten Criterion

Complex extremal surfaces naturally arise in holographic observables associated with timelike subregions in AdS/CFT and with holographic observables in dS/CFT, but their integration contours are generally ambiguous. In this work, we propose a method for constructing complex bulk metrics from families of complex extremal surfaces, thereby generating candidate complex geometries relevant to the gravitational path integral. This construction provides a concrete realization of how complex bulk geometry may emerge from timelike entanglement, extending the familiar idea that spacetime geometry is encoded in quantum entanglement. We use the Kontsevich--Segal--Witten (KSW) criterion as a strong consistency condition to constrain the corresponding contours. The same framework also explains why spacelike entanglement naturally selects a real Lorentzian section. In several AdS and dS examples, the KSW condition uniquely determines the admissible contour within the class considered. We also identify configurations for which the resulting complex geometry violates the KSW bound near the asymptotic boundary, revealing both the scope and the limitations of the construction. These results highlight KSW admissibility as a useful organizing principle for complex saddles in real-time holography.

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arXiv2025

Entanglement of General Subregions in Time-Dependent States

We develop a unified framework for computing Rényi and entanglement entropies of arbitrary spacetime intervals in time-dependent states of $(1+1)$-dimensional conformal field theories. By combining the spacetime density matrix formalism with the replica method, we show that entanglement entropy is well defined for both spacelike and timelike separations. Applying this framework to global quenches prepared by boundary states and to local quenches generated by operator insertions, we obtain analytic expressions for the entanglement entropy in general spacetime configurations. The results reveal qualitative differences between spacelike and timelike intervals: the timelike entanglement entropy is time-independent in the global quench model, depends solely on the temporal separation, and universally exhibits a constant imaginary contribution. These features are naturally explained by a generalized quasiparticle picture in which entanglement is produced precisely when one worldline of each quasiparticle pair intersects the interval. Furthermore, we demonstrate that the linear sum rule relating time- and spacelike entanglement persists in both global and local quenches, indicating a broader universality of spacetime entanglement in real-time quantum dynamics.

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arXiv2025

Relation between time- and spacelike entanglement entropy

In this study, we establish a connection between timelike and spacelike entanglement entropy. We show that timelike entanglement entropy is closely related to spacelike entanglement entropy and its temporal derivative. For a broad class of states, it can be uniquely determined by a linear combination of spacelike entanglement entropy and its first-order temporal derivative. This relation holds, for instance, in states conformally equivalent to the vacuum in two-dimensional conformal field theories. For more general states, we demonstrate that the relation can be constructed perturbatively. Our results suggest that timelike entanglement entropy is constrained by causality. Moreover, this relation provides a unified framework for timelike and spacelike entanglement entropy, within which the imaginary component of timelike entanglement entropy can be understood as arising from the non-commutativity between the twist operator and its first-order temporal derivative.

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arXiv2025

Duality of Ryu-Takayanagi surfaces inside and outside the horizon

We study the Ryu-Takayanagi (RT) surfaces associated with timelike subregions in static spacetimes with a horizon. It is possible to find the analytical continuation of the RT surfaces that can extend into the horizon, allowing us to probe the interior of the black hole. The horizon typically divides the RT surface into two distinct parts. We demonstrate that the area of the surface inside the horizon can be reconstructed from the contributions of the surfaces outside the horizon, along with additional RT surfaces for spacelike subregions that are causally related to the timelike subregions. This result provides a concrete realization of black hole complementarity at the level of classical metric, where the spacetime in the black hole interior can be reconstructed from the degrees of freedom outside the horizon.

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arXiv2025

Spacetime Density Matrix: Formalism and Properties

In this paper, we develop the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix defined on a single Cauchy surface. We present the construction of the spacetime density matrix in general quantum systems and its representation via the Schwinger Keldysh path integral. We further introduce a super-operator framework, within which the spacetime density matrix appears as a special case, and discuss possible generalizations from this perspective. We also show that the spacetime density matrix satisfies a Liouville von Neumann type equation of motion. When considering subsystems, a reduced spacetime density matrix can be defined by tracing over complementary degrees of freedom. We study the general properties of its moments and, in particular, derive universal short time behavior of the second moment. We find that coupling between subsystems plays a crucial role in obtaining nontrivial results. Assuming weak coupling, we develop a perturbative method to compute the moments systematically.

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arXiv2025

Quantum Entanglement Autodistillation in Baryon Pair Decays

We study the spin-entangled mixed state of a spin-1/2 baryon-antibaryon pair produced in the process e+e- to J/psi, psi(2S) to BBbar. We demonstrate that the spin entanglement of the system can increase following the decays B to b + M and Bbar to bbar + Mbar, where b and bbar are spin-1/2 baryons and M, Mbar are spin-0 mesons. This phenomenon, known as entanglement autodistillation, represents a probabilistic amplification of entanglement during the decay process. We analyze the underlying mechanism and show that it depends only on the initial state of the BBbar system and the decay parameter alphaD, but not on the phase parameter phiD.

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arXiv2025

Entanglement measures for causally connected subregions and holography

In this paper, we investigate entanglement for causally connected subregions $A$ and $B$ in quantum field theory and holography. Recent developments have established that a transition operator $T_{AB}$ can be well-defined for such subregions, which is generally non-Hermitian. By employing the Schwinger-Keldysh formalism and the real-time replica method, we show how to construct $T_{AB}$ and compute associated entanglement measures. In certain configurations, this leads to a notion of timelike entanglement entropy, for which we provide explicit quantum field theory computations and propose a holographic dual via analytic continuation from the Euclidean setup. Both analytical and numerical results are compared and found consistent. If entanglement between causally connected subregions is to be meaningful, it should also be able to define other entanglement measures. Motivated by the spacelike case, we propose a timelike extension of the entanglement wedge cross section, though we do not expect it to carry the same physical interpretation. In AdS$_3$/CFT$_2$, we compute explicit examples and find that the timelike entanglement wedge cross section is generally positive. Furthermore, we show that the reflected entropy for timelike intervals -- obtained via analytic continuation of twist correlators -- coincides with twice the timelike entanglement wedge cross section at leading order in $G$, supporting a holographic duality in the timelike case. We also discuss the extension of other entanglement measures, such as logarithmic negativity, to timelike separated regions using replica methods. We highlight conceptual challenges in defining reflected entropy via canonical purification for non-Hermitian operators.

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arXiv2025

Measuring the Black Hole Interior from the Exterior

In this essay, we argue that an observer outside the horizon can reconstruct the geometry of a black hole's interior through external measurements. This procedure builds on recent studies of the holographic duality of timelike entanglement entropy and its connection to spacelike entanglement entropy. Furthermore, we propose that this phenomenon reveals a fundamental correlation between the degrees of freedom inside and outside the black hole at the level of classical spacetime.

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arXiv2024

Imaginary part of timelike entanglement entropy

In this paper, we explore the imaginary part of the timelike entanglement entropy. In the context of field theory, it is more appropriate to obtain the timelike entanglement entropy through the Wick rotation of the twist operators. It is found that, in certain special cases, the imaginary part of the timelike entanglement entropy is related to the commutator of the twist operator and its first-order temporal derivative. To evaluate these commutators, we employ the operator product expansion of the twist operators, revealing that the commutator is generally universal across most scenarios. However, in more general cases, the imaginary part of the timelike entanglement entropy proves to be more complex. We compute the commutator of the twist operators along with its higher-order temporal derivatives. Utilizing these results, we derive a modified formula for the imaginary part of the timelike entanglement entropy. Furthermore, we extend this formula to the case of strip subregion in higher dimensions. Our analysis shows that for the strip geometry, the imaginary part of the timelike entanglement entropy is solely related to the commutators of the twist operator and its first-order temporal derivative. The findings presented in this paper provide valuable insights into the imaginary part of timelike entanglement entropy and its physical significance.

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arXiv2024

Spectral Projections for Density Matrices in Quantum Field Theories

In this paper, we investigate the spectral projection of density matrices in quantum field theory. With appropriate regularization, the spectral projectors of density matrices are expected to be well-defined. These projectors can be obtained using the Riesz projection formula, which allows us to compute both the density of eigenvalues and the expectation values of local operators in the projected states. We find that there are universal divergent terms in the expectation value of the stress energy tensor, where the coefficients depend universally on the density of eigenvalues and a function that describes the dependence of eigenvalues on boundary location. Using projection states, we can construct a series of new states in quantum field theories and discuss their general properties, focusing on the holographic aspects. We observe that quantum fluctuations are suppressed in the semiclassical limit. We also demonstrate that the fixed area state, previously constructed using gravitational path integrals, can be constructed by suitably superposition of appromiate amount of projection states. Additionally, we apply spectral projection to non-Hermitian operators, such as transition matrices, to obtain their eigenvalues and densities. Finally, we highlight potential applications of spectral projections, including the construction of new density and transition matrices and the understanding of superpositions of geometric states.

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arXiv2024

Pseudoentropy sum rule by analytical continuation of the superposition parameter

In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of a superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density matrix of the superposition state can be treated in a unified manner. Within this framework, we naturally derive sum rules for the (reduced) transition matrix, pseudo Rényi entropy, and pseudoentropy. Furthermore, we demonstrate the close relationship between the sum rule for pseudoentropy and the singularity structure of the entropy function for the superposition state after analytical continuation. We also explore potential applications of the sum rule, including its relevance to understanding the gravity dual of non-Hermitian transition matrices and establishing upper bounds for the absolute value of pseudoentropy.

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arXiv2024

Non-Hermitian spacetime and generalized thermofield double formalism

In this paper, we explore the non-Hermitian transition matrix and its gravity dual. States in quantum field theories or gravity theories are typically prepared using Euclidean path integrals. We demonstrate that it is both natural and necessary to introduce non-Hermitian transitions to describe the state when employing different inner products in Euclidean quantum field theories. Transition matrices that are $η$-pseudo-Hermitian, with $η$ being positive-definite, play the same role as density matrices, where the operator $η$ is closely related to the definition of the inner product. Moreover, there exists a one-to-one correspondence between these transition matrices and density matrices. In the context of AdS/CFT correspondence, the Euclidean path integral in the boundary field theory can be translated to the bulk gravitational path integral. We provide an overview of the construction and interpretation of non-Hermitian spacetime. Specifically, we demonstrate the crucial role of the non-Hermitian transition matrix in realizing the thermofield concept in general cases and in understanding the gravity states dual to the eternal black hole. In this context, the pseudoentropy of the transition matrix can also be interpreted as black hole entropy. Finally, we highlight the strong subadditivity property of pseudoentropy, and the connection between non-Hermitian transition matrices and complex metrics.

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arXiv2024

Sum rule for the pseudo-Rényi entropy

By generalizing the density matrix to a transition matrix between two states, represented as $|ϕ\rangle$ and $|ψ\rangle$, one can define the pseudoentropy analogous to the entanglement entropy. In this paper, we establish an operator sum rule that pertains to the reduced transition matrix and reduced density matrices corresponding to the superposition states of $|ϕ\rangle$ and $|ψ\rangle$. It is demonstrated that the off-diagonal elements of operators can be correlated with the expectation value in the superposition state. Furthermore, we illustrate the connection between the pseudo-Rényi entropy and the Rényi entropy of the superposition states. We provide proof of the operator sum rule and verify its validity in both finite-dimensional systems and quantum field theory. We additionally demonstrate the significance of these sum rules in gaining insights into the physical implications of transition matrices, pseudoentropy, and their gravity dual.

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arXiv2023

Parameter dependence of entanglement spectra in quantum field theories

In this paper, we explore the characteristics of reduced density matrix spectra in quantum field theories. Previous studies mainly focus on the function $\mathcal{P}(λ):=\sum_i δ(λ-λ_i)$, where $λ_i$ denote the eigenvalues of the reduced density matirx. We introduce a series of functions designed to capture the parameter dependencies of these spectra. These functions encompass information regarding the derivatives of eigenvalues concerning the parameters, notably including the function $\mathcal{P}_{α_J}(λ):=\sum_i \frac{\partial λ_i }{\partial α_J}δ(λ-λ_i)$, where $α_J$ denotes the specific parameter. Computation of these functions is achievable through the utilization of Rényi entropy. Intriguingly, we uncover compelling relationships among these functions and demonstrate their utility in constructing the eigenvalues of reduced density matrices for select cases. We perform computations of these functions across several illustrative examples. Specially, we conducted a detailed study of the variations of $\mathcal{P}(λ)$ and $\mathcal{P}_{α_J}(λ)$ under general perturbation, elucidating their physical implications. In the context of holographic theory, we ascertain that the zero point of the function $\mathcal{P}_{α_J}(λ)$ possesses universality, determined as $λ_0=e^{-S}$, where $S$ denotes the entanglement entropy of the reduced density matrix. Furthermore, we exhibit potential applications of these functions in analyzing the properties of entanglement entropy.

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arXiv2023

Pseudo entropy and pseudo-Hermiticity in quantum field theories

In this paper, we explore the concept of pseudo Rényi entropy within the context of quantum field theories (QFTs). The transition matrix is constructed by applying operators situated in different regions to the vacuum state. Specifically, when the operators are positioned in the left and right Rindler wedges respectively, we discover that the logarithmic term of the pseudo Rényi entropy is necessarily real. In other cases, the result might be complex. We provide direct evaluations of specific examples within 2-dimensional conformal field theories (CFTs). Furthermore, we establish a connection between these findings and the pseudo-Hermitian condition. Our analysis reveals that the reality or complexity of the logarithmic term of pseudo Rényi entropy can be explained through this pseudo-Hermitian framework. Additionally, we investigate the divergent term of the pseudo Rényi entropy. Interestingly, we observe a universal divergent term in the second pseudo Rényi entropy within 2-dimensional CFTs. This universal term is solely dependent on the conformal dimension of the operator under consideration. For $n$-th pseudo Rényi entropy ($n\ge 3$), the divergent term is intricately related to the specific details of the underlying theory.

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arXiv2023

Constructible reality condition of pseudo entropy via pseudo-Hermiticity

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.

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