Papers

We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local $\mathfrak{su}(D)$ exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling $\xi^2\propto1/N$ in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.

We study how much quantum structure bottomonium retains during its evolution in the quark-gluon plasma. Within the open quantum system framework, we simulate the Lindblad equation obtained from potential nonrelativistic QCD in the quantum Brownian regime. From the resulting real-time evolution of the bottomonium density matrix, we compute the Wigner transform and study its negativity as a measure of nonclassicality and a test of a key condition underlying classical Langevin-type approximations. We find that the medium suppresses the negativity, which nevertheless approaches a finite plateau close to that of the $1\mathrm{S}$ state. The overlaps with the excited $2\mathrm{S}$ and $3\mathrm{S}$ states arise from near-canceling positive and negative phase-space contributions, driven by negative regions in the Wigner transforms of the bound-state projectors, while the $1\mathrm{S}$ overlap is insensitive to such contributions. We further show that the position-space coherence is similarly suppressed and plateaus close to the 1S value. We trace the finite residual quantum structure to conditional purification: the medium preferentially dissolves weakly bound and unbound modes with large $\langle r^2\rangle$, driving the surviving singlet $\mathrm{S}$-wave ensemble toward the $1\mathrm{S}$ state. More broadly, these results reveal that classicalization is partial and observable dependent, a feature that is relevant across applications of open quantum system methods in fundamental physics.

Counterdiabatic driving provides a universal route to fast quantum control, but its standard formulation presupposes a Hamiltonian generator. We develop a Hamiltonian-free theory of the adiabatic gauge potential (AGP) for parameter-dependent unitary operators $U_\lambda$. Exact and regularized versions of the AGP follow from a Hermitian, banded linear system at a cost comparable to the Lanczos construction in the Hermitian case, requiring neither diagonalization nor a matrix logarithm. We demonstrate rapid convergence of the truncated Krylov approximation for the kicked top and for an integrable brickwork circuit built from unitary $\check{R}$ matrices, a setting in which no local effective Hamiltonian is available. Our results extend shortcuts to adiabaticity, and AGP-based diagnostics of chaos, to Floquet systems and quantum circuits.

Line-intensity mapping (LIM) is an emerging technique for probing both the astrophysics of galaxy formation and the cosmological evolution of large-scale structure. We investigate, for the first time, its potential as a probe of dark matter-baryon (DM-$b$) interactions using the upcoming Carbon Monoxide Mapping Array Project (COMAP) surveys, COMAP-EoR (Epoch of Reionization) and COMAP-ERA (Expanded Reionization Array). Elastic scattering of dark matter (DM) with baryons, i.e., protons ($p$) and electrons ($e$), exchange momentum and heat with the DM, suppressing structure formation and leaving characteristic signatures in the linear matter power spectrum. These effects propagate to the LIM power spectrum (PS) and voxel intensity distribution (VID). We consider momentum-transfer cross sections $\sigma^{\chi b}_{T,n}=\sigma^{\chi b}_{n}v^n$, with $n=0,-2,$ and $-4$, corresponding to contact, electric dipole-moment-like, and Coulomb-like interactions, respectively. Using Fisher forecasts, we obtain the projected sensitivities to $\sigma^{\chi b}_{n}$ from the PS and VID. Our VID-only forecasts combining the 16 and 30 GHz observed bands yield stronger sensitivities than existing cosmological limits for $n=-2$ and $n=-4$ for sub-GeV DM masses. We also explore the potential of combining the PS and VID to probe these interactions. Our study highlights LIM as a complementary probe of DM models alongside other astrophysical, cosmological, and terrestrial searches.

Random projective measurements are an effective tool to model the interlinked phenomenology of monitoring, inferring, and decoding highly entangled states such as quantum error-correcting codes. At the same time, the study of such monitored dynamics has opened a new arena for critical phenomena, renewing longstanding questions in disordered statistical mechanics, including percolation, random-bond models, and Nishimori physics. Here we investigate the robustness of stabilizer quantum error-correcting codes under a single round of independently sampled single-qubit Pauli measurements and demonstrate that their threshold behavior falls into two broad categories - geometric and homological percolation transitions, with the toric code and color code being the principal examples for each class. We establish the distinct character of these two threshold theories by analyzing the logical-support criteria of these codes and by providing numerical estimates of their respective critical exponents obtained from optimized stabilizer simulations of large-scale systems with over one million qubits. Our framework extends to non-CSS, subsystem, higher-dimensional, and Floquet stabilizer codes and allows us to determine their respective threshold phase diagrams. We exemplify how the latter provide quantitative and qualitative guidance for the computationally more demanding problems of tunable learning and maximum-likelihood decoding. As a practical application of our framework, we discuss the robustness of the gross code.

We conjecture that the universal logarithmic coefficient for capacity of entanglement $c_{\mathrm{cap}}$ is bounded below by the corresponding entropy coefficient $c_{\mathrm{eff}}$ at conformal interfaces. We prove the bound in free boson and fermion CFTs and in holographic models with interface branes, and establish it using defect perturbation theory. Numerical calculations at interacting interfaces between the tricritical Ising and Ising CFTs further support the bound. Despite this constraint, capacity provides independent interface data. We construct interfaces with identical entropy and energy transmission coefficients but different capacity coefficients, and show that capacity can even increase as entropy decreases.

Galactic magnetic fields are thought to be seeded by microscopic processes such as the Biermann battery and are primarily amplified to observed microgauss strengths by dynamo processes. Much of this amplification likely occurs within proto-galaxies, where turbulent and rotational kinetic energy is converted into magnetic energy via dynamo action. However, two aspects of this process remain poorly constrained in simulations: the saturation level of the amplified field and the timescale on which it is reached. In particular, different numerical methods, resolution strategies, and subgrid prescriptions have not converged to similar results, making it difficult to establish robust, code-independent conclusions about dynamo amplification in galaxies. In this work, we present the first systematic comparison of both Eulerian and Lagrangian codes that employ diverse MHD schemes, including ART, RAMSES, AREPO, and SWIFT. Using identical initial conditions for Milky Way-type galaxies and without including star formation and stellar feedback, we find that the amplification history of the magnetic field within the galactic disk depends strongly on the choice of hydrodynamical scheme, with orders-of-magnitude differences between Eulerian and Lagrangian approaches. We further demonstrate that reducing the mesh velocity in the moving-mesh code AREPO leads to results consistent with those obtained using the static grid codes ART and RAMSES. These results highlight the importance of carefully assessing numerical effects when interpreting magnetic field amplification in galaxy simulations.

We study the entanglement structure of partially entangled thermal states in double-scaled SYK , allowing flavor degrees of freedom carried by matter insertions to be in an arbitrary mixed state. In the semiclassical limit, followed by the heavy-probe limit, our replica calculation gives a Faulkner–Lewkowycz–Maldacena formula: the boundary entropy decomposes into an `area' term (independent of the flavor state) and the bulk matter entropy in a corresponding entanglement wedge. Varying the Euclidean locations of the operator insertions produces sharp transitions in the boundary entropy, which we interpret as individual matter excitations crossing the boundary of the wedge and hence as evidence for a sharply defined entanglement wedge. To derive this result, we analyze the semiclassical behavior of general Euclidean $2n$-point functions and give a probabilistic proof of their factorization into sums over products of two-point functions. We also give a complementary derivation from exact spectral representations, using the semiclassical behavior of the quantum $6j$-symbol.

The supersymmetric index, which gives a signed count of the microstates of black holes, can be computed directly from a gravitational path integral with appropriate boundary conditions. From general arguments based on the supersymmetry algebra, the index is expected to be independent of the temperature and, away from walls of marginal stability, of the asymptotic values of the scalar moduli. On the gravity side, this has been verified by explicit computations in many examples, but a general proof is lacking even at the classical level. We fill this gap by showing that in any four-dimensional supergravity theory with $\mathcal{N} \geq 2$ supersymmetry in asymptotically flat space-time, the classical contribution to the index from each supersymmetric saddle is independent of both. The argument uses only the behavior of the solution and of the Killing spinor equations near infinity. The result therefore holds in the presence of arbitrary higher-derivative corrections and for multi-centered black hole configurations. In particular, moduli independence follows without appeal to the attractor mechanism, which relies on the near-horizon geometry.

We study the thermodynamics of the BMN matrix model at large $N$ and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional $SO(9)$ gauged supergravity, the static $SO(3)\times SO(6)$-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of $\mu/T$, which power-law fits place at $4\pi$ with an estimated uncertainty below $10^{-10}$. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the $2/5$ power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.

The measurement of primordial CMB B-mode polarization is fundamentally limited by our ability to separate this faint signal from bright and complex Galactic foregrounds. Spectral Matching Independent Component Analysis (SMICA) offers a flexible, semi-blind approach to this foreground-cleaning problem. However, its standard implementation relies on a physically unrealistic assumption of non-spatially varying foreground emission, reducing the efficiency of the method. In this work, we develop two complementary strategies to address this limitation at the component-separation level. First, we augment SMICA with effective foreground components beyond the physical dust and synchrotron degrees of freedom. Second, we extend SMICA to operate independently on subsets of the sky, better capturing local variations in the foreground emission. Beyond component separation, we further explore a likelihood-level marginalization procedure using internally reconstructed foreground templates. We demonstrate the performance of the pipeline on simulated LiteBIRD-like observations, using foreground models of increasing complexity based on $\texttt{d1s1}$ and $\texttt{d10s5}$. Combining our component-separation improvements with template marginalization brings the recovered tensor-to-scalar ratio $r$ to effectively unbiased levels, with statistical uncertainties on the order of $10^{-3}$ or below.

Unital quantum channels are the noncommutative analogues of doubly stochastic matrices. In 1959, Marcus and Ree showed that the squared Frobenius norm of a doubly stochastic matrix is at most its maximal diagonal sum. We prove a quantum version of this inequality for mixed unitary channels on $\mathbb{M}_d$ and give an example showing that it fails for general unital channels. As in the classical case, we call the channels attaining equality as Erdős channels. We show that the trace-preserving conditional expectation onto any unital $C^*$-subalgebra of $\mathbb{M}_d$ is an Erdős channel. It is also locally isolated among channels of the same Choi rank. Next, we introduce quantum RCDS channels. These are the noncommutative analogue of doubly stochastic matrices whose supported permutations all have the same diagonal sum. We prove a structure theorem for them and use it to characterize the quantum RCDS Erdős channels. We give an explicit form, up to unitary equivalence, for the Erdős channels of Choi rank $2$, and further show that there are uncountably many unitary equivalence classes of Erdős channels unlike the classical case. We also characterize the Erdős channels among mixed Weyl-unitary channels of any Choi rank. For qubits, we prove that there are exactly four unitary equivalence classes of Erdős channels and they are represented by the identity channel and uniform averages of Pauli channels. Finally, restricting to the diagonal channels, our results recover the Marcus–Ree inequality, the structure of RCDS doubly stochastic matrices, and the characterization of Erdős.

Rotational variations in pulsars reflect either internal angular momentum exchange via equal and opposite torques (stationary spin noise) or independent torques causing diffusive changes in total angular momentum (nonstationary spin noise). We compare two models of a radio-emitting crust and interior superfluid to test the stationarity of angular velocity fluctuations through observed pulsar phases. We present results for three isolated pulsars with measurable timing noise, demonstrating distinct inference outcomes. For PSR J1359-6038, the data mildly favor independent torques over equal-and-opposite torques, with an odds ratio of seven hundred to one. For PSR B1937+21, the analysis shows no clear preference between the models. For Vela in a pre-glitch interval, excess scatter and unexplained residual structure limit the interpretation.

Local fermionic mode (LFM) based quantum computation has pure state spaces that are isomorphic, via the Jordan-Wigner representation, to qubit state spaces, but its compositional structure is subtly different. Indeed, the algebraic formalism specifying how to embed fermionic systems underlies a notion of parallel composition, for which, in general, the usual interchange law of monoidal categories fails. We give a categorical account of this phenomenon. Starting from the CAR-algebraic semantics of fermionic gate application, we show that LFM processes form a symmetric premonoidal category whose centre is precisely the even, parity-preserving subcategory. The same processes can alternatively be organized with the ordinary tensor product and a fermionic presymmetry that is natural exactly on even maps. To reason diagrammatically in this latter presentation, we introduce pronaps, a relaxation of the notion of prop, in which permutations are not-necessarily-natural, and use them to organize a hierarchy of fragments of the fermionic ZW calculus relevant to the study of fermionic circuits on physically motivated gate-sets. We then extend scalable diagrammatic notation to pronaps. In this setting, syntactic sugars inspired by SZX and GSA are defined, with the specificity that matrix arrows encode minors and determinants, while graph triangles encode pfaffians of principal submatrices. These constructions yield elegant normal forms and completeness proofs for our presentations of the EoW, FoW, EW, and FW fragments. In particular, the FW presentation gives a new normal form for the matchgate fragment, distinct from the rWGS-X normal form of the planar-W (pW) presentation of the same category. The resulting framework connects fermionic circuit semantics, diagrammatic rewriting with scalable notations, and the algebra of determinants and pfaffians.

Much of quantitative science involves difficult mathematical computations: a Feynman integral, evidence for an evolutionary tree, or a regulatory statistic. These are often estimated by Monte Carlo or heuristic search, or computed in floating point without tracking rounding error. Exact methods often exist, but in a field far from the problem. The reduction methods of collider physics also work on a Bayesian evidence, and a regulatory threshold can be settled with interval arithmetic from numerical analysis, but few people know both fields. A large language model knows both, and every other field, and with working programs in hand it can carry a method from one to another. BootLoops is a pool of such programs: integral reduction, differential equations and high-precision evaluation from particle physics, integer-relation fitting from experimental mathematics, exact enumeration, and ball arithmetic, in one toolkit that any agentic large language model can operate and extend. These tools can compute multi-loop Feynman integrals by bootstrap methods rather than direct integration, across the function classes that arise, including polylogarithms, elliptic functions, and periods of K3 surfaces and Calabi-Yau manifolds. They can also evaluate Bayesian evidence integrals as exact rational numbers, enumerate finite configuration spaces with proof of completeness, show when a sought closed form cannot exist, and redo floating-point calculations with guaranteed digits. In practice this brings the tools of mathematics, computer science and physics to problems in genomics, statistics, ecology and other fields. The toolkit and its documentation are at https://bootloops.ai.

Electromagnetic properties of materials are commonly inferred from how they scatter light. Here we show that this diagnostic is fundamentally incomplete. We predict the existence of an intrinsic electromagnetic property that remains invisible in any scattering experiment independently of geometry, polarization, far-field or near-field excitation. Still, this property affects the radiation emitted by the sources embedded inside the material. We reveal this phenomenon for a specially designed nonreciprocal magnetoelectric material combining axion and dual axion responses. Our results establish intrinsic electromagnetic properties as a distinct class of material responses and show that scattering experiments alone are insufficient to characterize matter.

I argue against the proposal of arXiv:2609.35787 to divide arXiv astrophysics submissions into two streams: peer-reviewed papers and pre-review discussion drafts. I contend that such a division would threaten open scientific discussion and could lead to increasingly restrictive categories based on journal impact factor or mainstream versus non-mainstream papers. Instead, readers who want only peer-reviewed work can use AI or other tools to filter papers, while others can continue monitoring the broader literature. I emphasize three benefits of posting papers on arXiv before journal acceptance. First, public posting lets researchers beyond the referee provide feedback, including identifying possible errors, missing references, and overlooked prior work, improving manuscripts beyond what a single referee may catch. Second, arXiv can help address weaknesses in the traditional anonymous peer-review system, such as lengthy delays, inconsistent reports, or unjustified rejection. Public posting establishes a transparent record of priority and allows the community to access results immediately. Finally, I propose that astrophysics journals require authors to post their papers on arXiv for at least a week before acceptance, making arXiv the central component of the astrophysical publication process.

We study the spherical geometry from the Simpson-Visser prescription $r\to\sqrt{r^2+a^2}$ to the quantum Oppenheimer-Snyder-Datt (qOSD) black hole of loop quantum cosmology, whose lapse function $A=1-2M/R+\alpha M^2/R^4$ carries the correction $\alpha$. This family interpolates between the qOSD black hole ($a\to0$), the Simpson-Visser black bounce ($\alpha\to0$), and Schwarzschild. The geometry is regular for every $a>0$, the Ricci scalar at the throat is blind to $\alpha$ while the Kretschmann scalar is not, and the null energy condition is violated at the throat by $-1/(4\pi a^2)$. The $(\alpha,a)$ plane splits into a two-horizon regular black hole, a single-horizon black hole with a hidden bounce, no Cauchy horizon, and a traversable wormhole; the middle region removes the mass-inflation channel of regular black holes without fine tuning. Because circular orbits are governed by the areal radius, photon sphere, shadow, ISCO and azimuthal epicyclic frequency depend on $\alpha$ only, whereas the Lyapunov exponent and radial epicyclic frequency carry the factor $\sqrt{1-a^2/R^2}$: shadow constrains only $\alpha$, while ringdown damping and the twin-peak quasiperiodic-oscillation ratio are sensitive to $a$. We derive horizon thermodynamics with a first-law entropy that departs from the area law, show that the bounce changes the thermodynamic topological charge from $W=-1$ to $W=0$ at every $\alpha$, and compute scalar, electromagnetic and Dirac quasinormal spectra using third-order WKB, Chebyshev spectral collocation and time-domain integration, which agree with one another and with eikonal scaling. Greybody bounds, Hawking emission, cascade sparsity and ringdown quality factor complete the analysis, and in the wormhole region the double-peaked potential produces echoes.

We describe construction of gravitationally dressed observables in de Sitter (dS) space, to leading non-trivial order in Newton's constant. We show that for an underlying field theory observable to be "gravitationally dressable," it must be dS invariant. If it satisfies this condition, its gravitational dressing can be constructed in terms of certain Green functions, by solving the condition that the dressed observable commute with the constraints. We provide a construction of the Green functions relevant for dressing observables lying on a time-symmetric slice. A simple example of a dS invariant observable is an operator creating a two-particle state of scalars. In the large mass limit, the particles are shown to be antipodally located, and the dressing of this operator (or corresponding state) can be explicitly constructed. Its behavior is diagnosed by certain correlators involving this state, and we check explicitly that these correlators then reproduce a linearized version of the Schwarzschild-dS solution. The underlying dS-invariant observables may be thought of as relational, and we argue can be generalized to include systems with properties of observers, which then could be likewise gravitationally dressed. We also briefly describe how such dressed observables can be related to alpha vacua, and discuss other questions regarding a more complete construction and role of such operators.

We present SW1D, a Python version of a legacy code for the forward computation of Rayleigh and Love wave dispersion curves as well as synthetic seismograms, in elastic, isotropic, laterally homogeneous media. This code solves the surface wave eigenvalue problem for 1-D media using a propagator-matrix technique and subsequently obtains surface wave excitations, in the frequency domain, for a point source described by its moment tensor. SW1D is validated through rigorous theoretical analyses and benchmarked against a well-established seismological software package. Ultimately, we demonstrate its place within an ecosystem of Python-based seismological tools designed for niche applications such as modelling surface wave propagation across lateral discontinuities, or forward modelling of ambient noise cross-correlations with arbitrary spatial distributions of ambient seismic sources.

Nearest-neighbor (NN) tight-binding models (TBMs) on plaquette-centered $\{ 10,3\}$ (Schläfli symbol), $\{ 8,3\}$, and $\{ 8,4\}$ hyperbolic lattices on a Poincaré disk with open boundary conditions display a vanishing, a finite, and a diverging density of states (DOS) near zero energy (band center), respectively, yielding a Dirac liquid, a Fermi liquid, and a flat band. Emergent bipartite nature of these lattices within the framework of NN-TBMs, allows us to scrutinize the impact of mass disorder on the electronic states and DOS therein. From extensive numerical calculations of the average and typical DOS using the kernel polynomial method, we show that hyperbolic Dirac liquid remains stable against weak mass disorder, undergoing a semimetal-to-metal quantum phase transition at moderate disorder, followed by an Anderson metal-to-insulator transition at even stronger disorder. The remaining two systems display only the latter transition. Critical exponents near all these transitions are found to be close to the ones mediated by on-site potential disorder.

We study Hamiltonian learning in a novel setting, where we are promised a physical structure that is obfuscated by a global unitary. In particular, we consider the task of learning the weights $E_i$ of a Hamiltonian $H=U^{\dagger}(\sum_{i \in I} E_i n_i + H_O)U$ comprised of a set of non-interacting modes $I$ and an arbitrary “spectator” $H_O$ acting on a disjoint set of modes $O$. The non-interacting structure is hidden by an unknown global unitary $U$, and our goal is to recover the $E_i$ without reconstructing $U$. Such Hamiltonians are well-motivated in the setting of materials modeling, where they find application for classical methods such as mean-field theory, Green's functions, and density functional theory. We show that this problem is DQC1-hard, despite the apparent simplification given by the non-interacting structure. We then introduce SPICES (single-particle inference via contour estimators), which combines a Hadamard test with a novel classical postprocessing procedure to efficiently recover the spectral distribution in Wasserstein distance under certain natural assumptions. The method exploits the correspondence between single-particle energies of the individual quasiparticles and the Fourier frequencies governing zeros of the partition function at complex inverse temperature. As quasiparticle spectra feature ubiquitously in downstream materials calculations, and with SPICES being simple and practical to execute, we expect that SPICES is a promising route to quantum applications in materials simulation.

We study the problem of learning the dense Sachdev–Ye–Kitaev (SYK) Hamiltonian from copies of its Gibbs state. Existing algorithms for Hamiltonian learning typically rely on geometric locality or bounded interaction degree and therefore do not apply to SYK, where each quartic interaction overlaps with $\Theta(n^3)$ others. We show that this obstruction can be overcome by exploiting the random mean-field structure of the model. At any constant temperature, we prove that with high probability over the SYK couplings, the entire Hamiltonian can be learned to inverse-polynomial accuracy using polynomially many samples. Furthermore, when the inverse temperature is restricted to be a sufficiently small constant, we construct a quasipolynomial-time learning algorithm which is qualitatively different from the sample-efficient algorithm.

Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.

The power and limitations of classical simulation are central to understanding quantum computational advantages. A leading simulation paradigm is based on coherent decomposition into classically tractable free states where the decomposition rank determines the simulation complexity. Proving strong lower bounds on this number is a notoriously difficult and mathematically rich problem, as exemplified by the qubit stabilizer rank problem. Here, we study the Gaussian version of this problem in both bosonic and fermionic systems and establish robust exponential lower bounds on Gaussian rank. In particular, we prove that for every pure non-Gaussian state on finitely many modes, with definite parity in the fermionic case, the approximate border Gaussian rank of its tensor powers grows at least exponentially at any fixed norm error below one. Our proofs combine reduction to four modes with Majorana spectral bounds for fermions, and Gaussian postselection with an entropy-based rank bound for bosons. As concrete examples, we derive explicit exponential lower bounds for the four-mode fermionic GHZ state and the bosonic single-photon state. The bosonic results require no assumption on the energy of the target state. Our results show that non-Gaussianity universally entails exponential Gaussian decomposition complexity, setting fundamental limitations on decomposition-based classical simulation of bosonic and fermionic systems.

We present a technique for computing Drell-Yan lepton pair production at particle-level that achieves N$^3$LO and approximate N$^4$LL$'$ accuracy at small to moderate transverse momentum, tree-level precision for $Z+4$, $5$, and $6$ jets, and approximate NLO EW precision at high transverse momentum. A crucial non-perturbative input, the Collins-Soper kernel, is obtained from continuum-limit lattice QCD results. High-precision theory results are recast into strictly positive event weights using an information-theoretic approach based on the maximum entropy principle.

We propose an extension of the cosmological-state construction of Antonini, Sasieta and Swingle (AS$^2$) to three or more holographic CFTs. Each CFT resides on the asymptotic boundary of an AdS page, and all pages are glued along a common interface by imposing the multiway junction conditions. The associated states are prepared by Euclidean evolution with a multilinear insertion. In appropriate heavy insertion limit the bulk geometry develop a closed universe in the center and we refer the state in this limit as a booklet cosmological state. Extending the effective Gaussian assumption used in AS$^2$, we model the three-page insertion by a circular complex Gaussian random tensor, yielding a tripartite Haar state in flat energy windows. In this Gaussian model of the cosmology-to-boundary map, each arm is a network branch associated with one boundary CFT. In the simplest example of three pages with three equal output Hilbert-space dimension $b$, we show that a prescribed code of dimension $K$ is approximately recoverable from any two arms, with vanishing error and high probability as $K/b\to0$.

Quantum impurity models are paradigmatic models of interacting quantum matter, as well as key computational primitives for modern electronic-structure methods. They describe a small subsystem of interacting fermions coupled to a large, noninteracting bath. We perform a comprehensive study of the computational complexity of simulating impurity models, delineating the boundary between classical and quantum tractability for this class of problems. Our main finding is that static properties of quantum impurity models can be calculated efficiently on a classical computer. Specifically, we give classical algorithms that (1) estimate the ground-state energy to additive precision $\delta$ in time $\mathrm{poly}(n,\delta^{-1})$, and (2) estimate the partition function at inverse temperature $\beta$ to relative precision $\delta$ in time $\mathrm{poly}(n,\beta,\delta^{-1})$, where $n$ is the system size. These results improve the previous best-known complexity for ground-state energy estimation from quasipolynomial to polynomial time, while establishing for the first time rigorous polynomial-time guarantees for simulating impurity models in thermal equilibrium. On the other hand, we find that simulating dynamical properties of impurity models is hard for classical computers but easy on a quantum computer. As a canonical example, we show that computing their nonequilibrium Green's functions captures the full power of quantum computation, even at finite temperature. Taken together, our results rule out superpolynomial quantum speedups for computing static properties, but provide an avenue for quantum advantage in simulating impurity physics out of equilibrium.

We introduce a method for studying state preparation complexity in dense quantum $p$-spin Hamiltonians on $n$ qubits, going beyond bounds based only on circuit lightcones. The key input is the class's effective profile complexity, which is derived from the metric entropy of its Pauli profiles. These profiles record expectations of all Pauli operators supported on exactly $p$ qubits. Classes with uniformly bounded quadratic effective profile complexity remain separated from the ground-state energy by a positive multiple of $\sqrt n$ for sufficiently large fixed $p$. At subquadratic effective profile complexity, the class cannot outperform a suitable benchmark class at leading order, with product states providing a universal benchmark. The proof combines an adaptation of a nonsymmetric quantum de Finetti theorem of Berta et al. (arXiv:1810.12197) with Gaussian process entropy bounds. Applying this framework, we show that attaining near-ground-state energy requires $\Omega(n^2/\log n)$ one- and two-qubit gates, even with arbitrary discardable ancillas. We also obtain depth-width tradeoffs, entanglement-depth and matrix product state bond-dimension lower bounds, and obstructions for both orientations at every fixed level of Parham's magic hierarchy (arXiv:2504.19966), with total circuit width $O(n)$. In first-level reverse magic, a shallow circuit is followed by an unrestricted Clifford circuit. The latter can spread local observables across the system, preventing a direct application of small-lightcone bounds. For this first-level class, our bounds also allow arbitrarily many clean ancillas at fixed shallow-circuit depth. A sharper benchmark shows that Clifford+$T$ circuits with $o(n)$ $T$-gates have no leading-order energy advantage over product stabilizer states, even with unrestricted Clifford operations and arbitrary discardable ancillas.

Hamiltonian learning provides a systematic framework for reconstructing unknown quantum dynamics. However, existing protocols typically assume direct measurement access to the entire system. With fast single-qubit control and a connected reference backbone, we show that a single measurable qubit suffices to learn all $O(N)$ independent parameters of a bounded-degree two-body Hamiltonian on $N$ qubits at the Heisenberg limit. Crucially, our protocol uses robust SWAP gates synthesized by quantum signal processing, enabling coherent transfer of states evolving under distant Hamiltonian parameters to the measurable qubit. This transfer requires no prior calibration of the Hamiltonian parameters of the intermediate links. A parallel learning architecture achieves total query time $\widetilde{O}(N)$ for an $N$-qubit chain, while retaining Heisenberg-limited precision scaling. On the chain, these scalings match the fundamental precision and information-propagation lower bounds up to logarithmic factors. The framework further extends to arbitrary bounded-degree interaction graphs. Our results establish a scalable route to learning an extensive number of many-body Hamiltonian parameters through only a local measurement interface.