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:2604.21755

Quantum-information diagnostics of cosmological perturbations with nontrivial sound speed in inflation

Shi-Cheng Liu, Lei-Hua Liu, Bichu Li, Hai-Qing Zhang, Peng-Zhang He

gr-qcastro-ph.COhep-phhep-thquant-phSubmitted Apr 23, 2026• Announced Apr 24, 2026• 0 citations
arXivHTMLPDF

Abstract

In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schrödinger evolution of the squeezing parameters ($r_k$ and $φ_k$). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, Rényi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable $x = \tanh r_k$ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.

Comments
33 pages, 5 figures

Related papers

Information-Theoretic Constraints on Cosmological Classicalization

Ayoub Taoussi

Description This work proposes an information-theoretic framework for describing the quantum–classical transition during cosmological inflation through open quantum system dynamics and entanglement evolution. The study introduces a normalized Quantum Persistence Function (QPF) as a scale-invariant diagnostic measure of residual quantum coherence, formulated in representation-independent form using reduced density matrix purity and entropy growth. The framework connects microscopic decoherence processes with macroscopic cosmological observables by applying spin–boson open-system dynamics to inflationary perturbations. Classical emergence is interpreted as a dynamical suppression of quantum coherence driven by entanglement entropy growth between cosmological modes rather than by simple interference cancellation. Observational constraints from primordial Gaussianity bounds are used to derive an efficiency condition for decoherence during reheating, expressed as a lower bound on the decoherence functional. The results show that classicalization occurs well below holographic entropy saturation limits, suggesting that cosmological classical emergence is governed primarily by dynamical information redistribution rather than fundamental information capacity thresholds. This work is deposited on Zenodo as an open scientific preprint to encourage constructive discussion and feedback from the scientific community. KEYWORDS: Quantum classical transition; decoherence theory; inflationary cosmology; open quantum systems; entanglement entropy; cosmological perturbations; quantum persistence function; information theory in physics; primordial fluctuations; classical emergence dynamics

•Feb 28, 2026•0 citations

Inflation is Not Magic

S. Shajidul Haque, Ghadir Jafari, Bret Underwood

Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter $f_{NL}$, but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."

hep-thCross-listedarXiv:2512.10126•Dec 12, 2025•0 citations

A Diagnostic Persistence Functional for Quantum Decoherence in Inflationary Perturbations

Ayoub Taoussi

Description : This work introduces a novel, model-independent diagnostic framework for quantifying quantum decoherence in primordial inflationary perturbations. The study addresses the fundamental problem of the quantum-to-classical transition in cosmology by defining a normalized persistence functional that captures the suppression of quantum coherence over time. Within an open quantum system approach, each perturbation mode is treated as an effective quantum degree of freedom interacting with an environment, leading to Gaussian suppression of off-diagonal density matrix elements. The proposed functional provides a direct and scalable measure of decoherence efficiency without relying on detailed microscopic modeling. A key feature of the framework is the introduction of a residual coherence parameter, which accounts for possible late-time deviations from complete classicalization. The work further establishes a monotonicity property for the decoherence functional and connects the persistence measure to entropy growth, offering an information-theoretic interpretation of the decoherence process. Importantly, the framework suggests a phenomenological link between residual coherence and observable non-Gaussianity in the cosmic microwave background, opening a pathway for potential observational constraints. The proposed diagnostic functional is broadly applicable across inflationary models and provides a unified tool for comparing decoherence efficiency under different environmental interactions. This work lays the foundation for future studies on quantum signatures in cosmological observables and the persistence of quantum features in the early universe. Keywords : Quantum Decoherence Inflationary Cosmology Primordial Perturbations Open Quantum Systems Quantum-to-Classical Transition Non-Gaussianity Cosmological Perturbation Theory Density Matrix Quantum Cosmology Early Universe Physics Decoherence Functional Entropy and Information Theory

•Apr 2, 2026•0 citations

A Diagnostic Criterion for Decoherence Efficiency in Inflationary Perturbations

Ayoub Taoussi

This preprint develops a model-independent diagnostic framework for evaluating decoherence efficiency in inflationary curvature perturbations within an open quantum system formulation. The work does not introduce a new decoherence mechanism; instead, it constructs a normalized dimensionless functional intended to provide a systematic basis for comparing environmental decoherence scenarios in primordial cosmology. A persistence functional is derived to characterize the attenuation of off-diagonal density matrix components under inflationary expansion. Using a representative toy open-system model, the analysis demonstrates that the functional exhibits rapid suppression behavior associated with the exponential growth of comoving volume during inflation. The framework further suggests that residual quantum coherence may contribute to higher-order correlation functions of curvature perturbations. Accordingly, observational constraints on primordial non-Gaussianity may be interpreted as indirect lower bounds on decoherence efficiency. The formulation is intended as a diagnostic tool rather than a proposal of a new physical decoherence process. Keywords : Inflationary Cosmology Quantum Decoherence Primordial Perturbations Open Quantum Systems Classicality Non-Gaussianity

•Mar 5, 2026•0 citations

No Intrinsic Decoherence of Inflationary Cosmological Perturbations

Jen-Tsung Hsiang, B. L. Hu

After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.

arXiv:2112.04092•Universe•Jan 3, 2022•24 citations

Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation

Tao Li, Hai-Bing Fu

In this work, we investigate quantum complexity diagnostics of primordial curvature perturbations within the inflationary paradigm. We compare canonical scalar-field inflation with the modified gravity model $f(φ,R)$, focusing on the evolution of the two-mode squeezed state generated by the coupling between the $\vec{k}$ and $-\vec{k}$ momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength $r_k$ and squeezed angle $φ_k$, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. Specifically, we compute the Krylov complexity, Krylov entropy, Lanczos coefficients $b_n$, and an effective dissipative contribution $c_n$ within an open-system extension. Our numerical results demonstrate that the $f(φ,R)$ coupling enhances the squeezed strength relative to the canonical scalar field inflation. Since the Krylov complexity of the two-mode squeezed state is directly controlled by the mean pair number ($K=\sinh^2 r_k$), this enhancement leads to a smaller growth in Krylov complexity and related Krylov-space quantities. Furthermore, circuit complexity displays a more pronounced evolution in the $f(φ,R)$ framework, particularly after the horizon exit regime. Ultimately, our work sheds new light on the quantum complexity of modified gravity $f(φ,R)$.

hep-thCross-listedarXiv:2607.09408•Jul 13, 2026
In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schrödinger evolution of the squeezing parameters (rkr_krk​ and φkφ_kφk​). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, Rényi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable x=tanh⁡rkx = \tanh r_kx=tanhrk​ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.
Description This work proposes an information-theoretic framework for describing the quantum–classical transition during cosmological inflation through open quantum system dynamics and entanglement evolution. The study introduces a normalized Quantum Persistence Function (QPF) as a scale-invariant diagnostic measure of residual quantum coherence, formulated in representation-independent form using reduced density matrix purity and entropy growth. The framework connects microscopic decoherence processes with macroscopic cosmological observables by applying spin–boson open-system dynamics to inflationary perturbations. Classical emergence is interpreted as a dynamical suppression of quantum coherence driven by entanglement entropy growth between cosmological modes rather than by simple interference cancellation. Observational constraints from primordial Gaussianity bounds are used to derive an efficiency condition for decoherence during reheating, expressed as a lower bound on the decoherence functional. The results show that classicalization occurs well below holographic entropy saturation limits, suggesting that cosmological classical emergence is governed primarily by dynamical information redistribution rather than fundamental information capacity thresholds. This work is deposited on Zenodo as an open scientific preprint to encourage constructive discussion and feedback from the scientific community. KEYWORDS: Quantum classical transition; decoherence theory; inflationary cosmology; open quantum systems; entanglement entropy; cosmological perturbations; quantum persistence function; information theory in physics; primordial fluctuations; classical emergence dynamics
Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter fNLf_{NL}fNL​, but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."
Description : This work introduces a novel, model-independent diagnostic framework for quantifying quantum decoherence in primordial inflationary perturbations. The study addresses the fundamental problem of the quantum-to-classical transition in cosmology by defining a normalized persistence functional that captures the suppression of quantum coherence over time. Within an open quantum system approach, each perturbation mode is treated as an effective quantum degree of freedom interacting with an environment, leading to Gaussian suppression of off-diagonal density matrix elements. The proposed functional provides a direct and scalable measure of decoherence efficiency without relying on detailed microscopic modeling. A key feature of the framework is the introduction of a residual coherence parameter, which accounts for possible late-time deviations from complete classicalization. The work further establishes a monotonicity property for the decoherence functional and connects the persistence measure to entropy growth, offering an information-theoretic interpretation of the decoherence process. Importantly, the framework suggests a phenomenological link between residual coherence and observable non-Gaussianity in the cosmic microwave background, opening a pathway for potential observational constraints. The proposed diagnostic functional is broadly applicable across inflationary models and provides a unified tool for comparing decoherence efficiency under different environmental interactions. This work lays the foundation for future studies on quantum signatures in cosmological observables and the persistence of quantum features in the early universe. Keywords : Quantum Decoherence Inflationary Cosmology Primordial Perturbations Open Quantum Systems Quantum-to-Classical Transition Non-Gaussianity Cosmological Perturbation Theory Density Matrix Quantum Cosmology Early Universe Physics Decoherence Functional Entropy and Information Theory
This preprint develops a model-independent diagnostic framework for evaluating decoherence efficiency in inflationary curvature perturbations within an open quantum system formulation. The work does not introduce a new decoherence mechanism; instead, it constructs a normalized dimensionless functional intended to provide a systematic basis for comparing environmental decoherence scenarios in primordial cosmology. A persistence functional is derived to characterize the attenuation of off-diagonal density matrix components under inflationary expansion. Using a representative toy open-system model, the analysis demonstrates that the functional exhibits rapid suppression behavior associated with the exponential growth of comoving volume during inflation. The framework further suggests that residual quantum coherence may contribute to higher-order correlation functions of curvature perturbations. Accordingly, observational constraints on primordial non-Gaussianity may be interpreted as indirect lower bounds on decoherence efficiency. The formulation is intended as a diagnostic tool rather than a proposal of a new physical decoherence process. Keywords : Inflationary Cosmology Quantum Decoherence Primordial Perturbations Open Quantum Systems Classicality Non-Gaussianity
After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.
In this work, we investigate quantum complexity diagnostics of primordial curvature perturbations within the inflationary paradigm. We compare canonical scalar-field inflation with the modified gravity model f(φ,R)f(φ,R)f(φ,R), focusing on the evolution of the two-mode squeezed state generated by the coupling between the k⃗\vec{k}k and −k⃗-\vec{k}−k momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength rkr_krk​ and squeezed angle φkφ_kφk​, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. Specifically, we compute the Krylov complexity, Krylov entropy, Lanczos coefficients bnb_nbn​, and an effective dissipative contribution cnc_ncn​ within an open-system extension. Our numerical results demonstrate that the f(φ,R)f(φ,R)f(φ,R) coupling enhances the squeezed strength relative to the canonical scalar field inflation. Since the Krylov complexity of the two-mode squeezed state is directly controlled by the mean pair number (K=sinh⁡2rkK=\sinh^2 r_kK=sinh2rk​), this enhancement leads to a smaller growth in Krylov complexity and related Krylov-space quantities. Furthermore, circuit complexity displays a more pronounced evolution in the f(φ,R)f(φ,R)f(φ,R) framework, particularly after the horizon exit regime. Ultimately, our work sheds new light on the quantum complexity of modified gravity f(φ,R)f(φ,R)f(φ,R).