Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.15227

Cosmological Pseudo-Entropy

Manghang Limbu, Pramod Kamal Kharel, Rohit Bhattarai, Kiran Adhikari

gr-qchep-thquant-phSubmitted Jun 13, 2026• Announced Jun 16, 2026
arXivHTMLPDF

Abstract

We study pseudo entropy $\mathcal{S}$, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed $0.024 \leq c_s \leq 1$, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter $w$. In de Sitter space, $\mathrm{Re}(\mathcal{S})$ grows after horizon exit while $c_s$ controls its onset and saturates at late times. A similar saturation occurs in expanding-accelerating and contracting-decelerating backgrounds. In contrast, expanding-decelerating and contracting-accelerating backgrounds show large early-time $\mathrm{Re}(\mathcal{S})$ followed by oscillations after horizon re-entry. This happens because while the squeezing freezes, the squeezing angle doesn't. Unlike entanglement entropy, pseudo entropy possesses an imaginary part, $\mathrm{Im}(\mathcal{S})$, as well, which can encode the relative phase. $\mathrm{Im}(\mathcal{S})$ decays to zero in de Sitter and expanding-accelerating cases, but forms dense sub-Hubble oscillation bands in expanding-decelerating and contracting-accelerating backgrounds. Compared with entanglement entropy, Krylov complexity, and Nielsen circuit complexity, pseudo entropy captures otherwise hidden phase information; in the unsaturated regime, its slope is $\sqrt{2}$ times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is $w$-independent, pseudo entropy is sensitive to $w$ during the transition regime, making it a finer information theoretic diagnostic of cosmological dynamics.

Related papers

Quantum Information Dynamics of QED$_2$ in Expanding de Sitter Universe

Kazuki Ikeda, Yaron Oz

We study QED$_2$ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as $1/a(t)$ while the electric term grows as $g^2 a(t)$, sweeping the spectrum through a moving narrow-gap region in the $(τ,m)$ plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later $τ$ as the lattice spacing goes to zero, with current data favoring $τ_* \approx 3.1$, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED$_2$ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

hep-thCross-listedarXiv:2604.02777•Apr 6, 2026•0 citations

The first heat: production of entanglement entropy in the early universe

Sergei Khlebnikov, Akhil Sheoran

Abstract Entanglement entropy (EE) of a spatial region quantifies correlations between the region and its surroundings. For a free scalar in the adiabatic vacuum in de Sitter space the EE is known to remain low, scaling as the surface area of the region. Here, we study the evolution of entanglement after the universe transitions from de Sitter to flat space. We concentrate on the case of a massless minimally coupled scalar. We find numerically that, after the de Sitter stage ends, the EE and the Ŕenyi entropy rapidly grow and saturate at values obeying the volume law. The final state of the subsystem (region) is a partially thermalized state reminiscent of a generalized Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.

arXiv:1907.00487•Journal of High Energy Physics•Nov 1, 2019•1 citation

Pseudo entropy and topological phases of matter

Pramod Kamal Kharel, Manghang Limbu, Nabaraj Khatri +2 more

Entanglement entropy has proven to be a powerful probe of phenomena such as quantum chaos and phase transitions. Pseudo entropy is a recently proposed time-like generalization of an entanglement measure, motivated by de Sitter holography. In this work, we find that pseudo entropy can also serve as a novel probe for distinguishing topological phases of matter. For this, we consider the Su--Schrieffer--Heeger model as a representative example and investigate the averaged excess entropy $ΔS_{12}$, defined as the difference between pseudo entropy and the average entanglement entropy, across the topological-to-trivial and trivial-to-topological phase transitions. When the two states are in the same phase, we find that $ ΔS_{12}$ is non-positive under periodic boundary conditions, while for open boundary conditions, it is non-positive only when the system is sufficiently large. Moreover, we analyze ground-state quench protocols for topology-crossing quenches and find that the imaginary pseudo entropy tracks the critical times predicted by the Fisher zeros.

cond-mat.stat-mechCross-listedarXiv:2606.29311•Jun 30, 2026•0 citations

Quantum information dynamics of QED2 in expanding de Sitter universe

Kazuki Ikeda, Yaron Oz

A bstract We study QED 2 in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as 1/ a ( t ) while the electric term grows as g 2 a ( t ), sweeping the spectrum through a moving narrow-gap region in the ( τ , m ) plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later τ as the lattice spacing goes to zero, with current data favoring τ ∗ ≈ 3.1, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED 2 as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

Journal of High Energy Physics•Jul 22, 2026•0 citations

New holographic generalization of entanglement entropy

Yoshifumi Nakata, Tadashi Takayanagi, Yusuke Taki +2 more

We introduce a new quantity, called pseudo-entropy, as a generalization of entanglement entropy via postselection. We expect this quantity to provide a new class of order parameters in quantum many-body systems. In the anti--de Sitter space (AdS)/conformal field theory (CFT) correspondence, this quantity is dual to areas of minimal area surfaces in time-dependent Euclidean spaces which are asymptotically AdS. We call this geometric computation of pseudo-entropy via the $\mathrm{AdS}/\mathrm{CFT}$ the holographic pseudo-entropy. We study its basic properties and classifications in qubit systems. In specific examples, we provide a quantum information theoretic meaning of this new quantity as an averaged number of Bell pairs when the post-selection is performed. We also present properties of the pseudo-entropy for random states. We then calculate the pseudo-entropy in the presence of local operator excitations for both the two dimensional free massless scalar CFT and two dimensional holographic CFTs. We find a general property in CFTs that the pseudo-entropy is highly reduced when the local operators get closer to the boundary of the subsystem. We also compute the holographic pseudo-entropy for a Janus solution, dual to an exactly marginal perturbation of a two dimensional CFT and find its agreement with a perturbative calculation in the dual CFT. We show the linearity property holds for holographic states, where the holographic pseudo-entropy coincides with a weak value of the area operator. Finally, we propose a mixed state generalization of pseudo-entropy and give its gravity dual.

arXiv:2005.13801•Physical review. D/Physical review. D.•Jan 11, 2021•126 citations

Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity

Sergio E. Aguilar-Gutierrez

We investigate entanglement entropy between the pair of type II$_1$ algebras of the double-scaled SYK (DSSYK) model given a chord state, its holographic interpretation as generalized horizon entropy; particularly in the (anti-)de Sitter ((A)dS) space limits of the bulk dual; and its connection with Krylov complexity. The density matrices in this formalism are operators in the algebras, which are specified by the choice of global state; and there exists a trace to evaluate their von Neumann entropy since the algebras are commutants of each other, which leads to a notion of algebraic entanglement entropy. We match it in triple-scaling limits to an area computed through a Ryu-Takayanagi formula in (A)dS$_2$ space with entangling surfaces at the asymptotic timelike or spacelike boundaries respectively; providing a first-principles example of holographic entanglement entropy for (A)dS$_2$ space. This result reproduces the Bekenstein-Hawking and Gibbons-Hawking entropy formulas for specific entangling regions points, while it decreases for others. This construction does not display some of the puzzling features in dS holography. The entanglement entropy remains real-valued since the theory is unitary, and it depends on the Krylov spread complexity of the Hartle-Hawking state. At last, we discuss higher dimensional extensions.

hep-thCross-listedarXiv:2511.03779•Journal of High Energy Physics•Nov 7, 2025•3 citations
We study pseudo entropy S\mathcal{S}S, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed 0.024≤cs≤10.024 \leq c_s \leq 10.024≤cs​≤1, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter www. In de Sitter space, Re(S)\mathrm{Re}(\mathcal{S})Re(S) grows after horizon exit while csc_scs​ controls its onset and saturates at late times. A similar saturation occurs in expanding-accelerating and contracting-decelerating backgrounds. In contrast, expanding-decelerating and contracting-accelerating backgrounds show large early-time Re(S)\mathrm{Re}(\mathcal{S})Re(S) followed by oscillations after horizon re-entry. This happens because while the squeezing freezes, the squeezing angle doesn't. Unlike entanglement entropy, pseudo entropy possesses an imaginary part, Im(S)\mathrm{Im}(\mathcal{S})Im(S), as well, which can encode the relative phase. Im(S)\mathrm{Im}(\mathcal{S})Im(S) decays to zero in de Sitter and expanding-accelerating cases, but forms dense sub-Hubble oscillation bands in expanding-decelerating and contracting-accelerating backgrounds. Compared with entanglement entropy, Krylov complexity, and Nielsen circuit complexity, pseudo entropy captures otherwise hidden phase information; in the unsaturated regime, its slope is 2\sqrt{2}2​ times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is www-independent, pseudo entropy is sensitive to www during the transition regime, making it a finer information theoretic diagnostic of cosmological dynamics.
Quantum Information Dynamics of QED2_22​ in Expanding de Sitter Universe
We study QED2_22​ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as 1/a(t)1/a(t)1/a(t) while the electric term grows as g2a(t)g^2 a(t)g2a(t), sweeping the spectrum through a moving narrow-gap region in the (τ,m)(τ,m)(τ,m) plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later τττ as the lattice spacing goes to zero, with current data favoring τ∗≈3.1τ_* \approx 3.1τ∗​≈3.1, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED2_22​ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.
Abstract Entanglement entropy (EE) of a spatial region quantifies correlations between the region and its surroundings. For a free scalar in the adiabatic vacuum in de Sitter space the EE is known to remain low, scaling as the surface area of the region. Here, we study the evolution of entanglement after the universe transitions from de Sitter to flat space. We concentrate on the case of a massless minimally coupled scalar. We find numerically that, after the de Sitter stage ends, the EE and the Ŕenyi entropy rapidly grow and saturate at values obeying the volume law. The final state of the subsystem (region) is a partially thermalized state reminiscent of a generalized Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.
Entanglement entropy has proven to be a powerful probe of phenomena such as quantum chaos and phase transitions. Pseudo entropy is a recently proposed time-like generalization of an entanglement measure, motivated by de Sitter holography. In this work, we find that pseudo entropy can also serve as a novel probe for distinguishing topological phases of matter. For this, we consider the Su--Schrieffer--Heeger model as a representative example and investigate the averaged excess entropy ΔS12ΔS_{12}ΔS12​, defined as the difference between pseudo entropy and the average entanglement entropy, across the topological-to-trivial and trivial-to-topological phase transitions. When the two states are in the same phase, we find that $ ΔS_{12}$ is non-positive under periodic boundary conditions, while for open boundary conditions, it is non-positive only when the system is sufficiently large. Moreover, we analyze ground-state quench protocols for topology-crossing quenches and find that the imaginary pseudo entropy tracks the critical times predicted by the Fisher zeros.
A bstract We study QED 2 in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as 1/ a ( t ) while the electric term grows as g 2 a ( t ), sweeping the spectrum through a moving narrow-gap region in the ( τ , m ) plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later τ as the lattice spacing goes to zero, with current data favoring τ ∗ ≈ 3.1, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED 2 as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.
We introduce a new quantity, called pseudo-entropy, as a generalization of entanglement entropy via postselection. We expect this quantity to provide a new class of order parameters in quantum many-body systems. In the anti--de Sitter space (AdS)/conformal field theory (CFT) correspondence, this quantity is dual to areas of minimal area surfaces in time-dependent Euclidean spaces which are asymptotically AdS. We call this geometric computation of pseudo-entropy via the AdS/CFT\mathrm{AdS}/\mathrm{CFT}AdS/CFT the holographic pseudo-entropy. We study its basic properties and classifications in qubit systems. In specific examples, we provide a quantum information theoretic meaning of this new quantity as an averaged number of Bell pairs when the post-selection is performed. We also present properties of the pseudo-entropy for random states. We then calculate the pseudo-entropy in the presence of local operator excitations for both the two dimensional free massless scalar CFT and two dimensional holographic CFTs. We find a general property in CFTs that the pseudo-entropy is highly reduced when the local operators get closer to the boundary of the subsystem. We also compute the holographic pseudo-entropy for a Janus solution, dual to an exactly marginal perturbation of a two dimensional CFT and find its agreement with a perturbative calculation in the dual CFT. We show the linearity property holds for holographic states, where the holographic pseudo-entropy coincides with a weak value of the area operator. Finally, we propose a mixed state generalization of pseudo-entropy and give its gravity dual.
We investigate entanglement entropy between the pair of type II1_11​ algebras of the double-scaled SYK (DSSYK) model given a chord state, its holographic interpretation as generalized horizon entropy; particularly in the (anti-)de Sitter ((A)dS) space limits of the bulk dual; and its connection with Krylov complexity. The density matrices in this formalism are operators in the algebras, which are specified by the choice of global state; and there exists a trace to evaluate their von Neumann entropy since the algebras are commutants of each other, which leads to a notion of algebraic entanglement entropy. We match it in triple-scaling limits to an area computed through a Ryu-Takayanagi formula in (A)dS2_22​ space with entangling surfaces at the asymptotic timelike or spacelike boundaries respectively; providing a first-principles example of holographic entanglement entropy for (A)dS2_22​ space. This result reproduces the Bekenstein-Hawking and Gibbons-Hawking entropy formulas for specific entangling regions points, while it decreases for others. This construction does not display some of the puzzling features in dS holography. The entanglement entropy remains real-valued since the theory is unitary, and it depends on the Krylov spread complexity of the Hartle-Hawking state. At last, we discuss higher dimensional extensions.