Papers

We propose a new formula relating the rationalized Drinfeld associators obtained from the Knizhnik–Zamolodchikov equation to the quantum $6j$-symbols of the algebra $\mathcal{U}_q(\mathfrak{g})$: $ U_{q} = U \cdot \Phi^{KZ}_{\mathbb{Q}} $. We prove this relation in the case of the $\mathfrak{sl}_N$ Lie algebra for the tensor cube of the fundamental and the first symmetric representation. We also check it perturbatively for the $\mathfrak{sl}_N$ algebra for representations $[2]\otimes [1] \otimes [1]$, $[2]\otimes [2] \otimes [1]$, the non-trivial cases with multiplicities — $[2,1]^{\otimes 3}$, $[2,2]^{\otimes 3}$, and in the case of the $\mathfrak{so}_5$ Lie algebra for the tensor cube of the fundamental representation.

We study a heterogeneous diffusion process with a position-dependent diffusion coefficient in the presence of independent recruitment and mortality. This framework generalises heterogeneous diffusion under stochastic resetting, which is recovered as the special case of equal recruitment and mortality rates. At long times, the system approaches a non-equilibrium stationary state with a mean squared displacement that saturates to a value independent of the recruitment rate. Crucially, this saturation limit directly encodes the underlying transport regime via an effective exponent applied to the diffusion coefficient, and we characterise the non-trivial transition to this stationary regime. We further derive the mean first-passage time to a target and show that, for a fixed recruitment-to-mortality ratio, an optimal mortality rate minimises the search time. This "mortality-assisted search" effect is confirmed by numerical evaluation. Reinterpreting recruitment and mortality as infection and removal processes, we apply the model to epidemic spreading and show that a moderate removal rate can counter-intuitively accelerate, rather than delay, the arrival of infection at a new spatial region. Beyond epidemiology, our framework offers broad relevance to systems featuring concurrent particle creation and destruction, such as bacterial growth, tracer diffusion in reactive fluids, or cellular population dynamics in crowded environments.

We construct an explicit rational \(\mathrm{SL}_2(\mathbb C)\)-action on the underlying vector space of the rank-two \(\beta\gamma\)-system. The construction is motivated by Creutzig's branching decomposition with respect to \(L_{-1}(\mathfrak{sl}_2)\) and a rank-one Heisenberg vertex algebra. We realize the raising and lowering operators as residues of lattice-type fields, prove that they preserve the original \(\beta\gamma\)-system despite being defined on localizations, and establish their commutation relations and integrability. The resulting action commutes with the affine \(L_{-1}(\mathfrak{sl}_2)\)-action and all nonzero Heisenberg modes, while the Heisenberg zero mode serves as its Cartan operator. Each affine multiplicity space is thereby identified with \(V_n\otimes\mathcal F_{\mathrm{osc}}\), where \(V_n\) is the irreducible \(\mathrm{SL}_2(\mathbb C)\)-module of highest weight \(n\) and \(\mathcal F_{\mathrm{osc}}\) is the Heisenberg oscillator Fock space. Thus the Heisenberg charge decomposition is realized as the weight decomposition of \(V_n\). The infinitesimal action is not by vertex algebra derivations and does not preserve the symmetric conformal grading.

Despite purely local microscopic dynamics, nonequilibrium steady states can develop long-range correlations. We investigate this phenomenon in the boundary-driven symmetric simple exclusion process by relating its exact nonlocal large-deviation functional to finite-time thermodynamic irreversibility under weak time-dependent driving. Decomposing the long-range correlations into hydrodynamic modes, we find that the lag associated with the slowest mode satisfies an upper bound determined by the excess entropy production rate at each driving frequency. This bound is approached in the quasistatic limit, whereas progressively shorter-wavelength modes do not generally satisfy the corresponding bound. These results provide a quantitative connection between the curvature of the large-deviation functional, long-range correlations in the nonequilibrium steady state, and finite-time dissipation. Within the linear-response regime considered here, they indicate that the longest-wavelength hydrodynamic mode has a distinct relation between slow relaxation and thermodynamic irreversibility.

We establish a scale-invariant spatial non-collapse estimate for hypersurface-orthogonal timelike geodesic congruences. The result extends a previous Raychaudhuri-based construction in which a comparison estimate for the expansion was used to control the volume of domains transported along the congruence. The additional ingredient here is a quantitative estimate of the spatial distance distortion induced by the expansion and shear. Assuming that the initial spatial geometry is non-collapsed up to a scale $r_0$, and that the expansion, shear, and timelike Ricci curvature satisfy suitable uniform bounds, we obtain, before the first blow-up time of the Raychaudhuri comparison solution, \begin{equation*} \operatorname{Vol}_{h_\tau}\bigl(B_{h_\tau}(p_\tau,r)\bigr) \geq \kappa_{\mathrm{L}}(\tau)\, r^3, \end{equation*} where \begin{equation*} \kappa_{\mathrm{L}}(\tau) = \kappa_0 e^{-3K\tau} \exp\!\left(\int_0^\tau \Theta(s)\,ds\right), \qquad K = \frac{\Theta_0}{3} + \Sigma_0 . \end{equation*} Here $\Theta$ denotes the solution of the scalar Raychaudhuri comparison equation and $K$ controls the spatial metric distortion. For every finite time strictly before the comparison barrier, $\kappa_{\mathrm{L}}(\tau)$ is positive. When the comparison solution has a finite blow-up time, the explicit comparison coefficient approaches zero as that time is approached from below. The comparison barrier is a boundary of the estimate and is not, by itself, a statement that the physical congruence develops a focal point or spacetime singularity. The result is structurally analogous to scale-invariant non-collapse estimates in geometric flow, but is mathematically distinct from Perelman's $\kappa$-noncollapsing theorem for Ricci flow.

The eigenstate quantum-mechanical bootstrap can converge to the physical moment set while remaining nonexact at every finite order. We prove this for a one-dimensional quasi-exactly solvable sextic oscillator at explicitly known eigenvalues, including excited levels. At every finite order, the lower and upper bounds on $u^2$ remain strictly below and above its physical value, even after adjoining arbitrary finite polynomial Gram tests and all eigenstate-annihilator relations visible in the retained moment space. Hence neither side of the centered observable admits a finite sum-of-squares certificate modulo the eigenstate annihilator. The gap persists under any finite set of additional localizing constraints whose weights are strictly positive on polynomial vectors. We then prove convergence for polynomial Schrödinger operators satisfying explicit sum-of-squares confinement and derivative bounds. The eigenstate relations give moment estimates uniform in the truncation order; these yield a regular Schrödinger representation supported on the prescribed eigenspace. Finally, a four-mode extension combines this fixed-observable obstruction with feasible position moments having no positive representing measure at every finite order. At level three, this construction yields nonphysical feasible points with strictly positive definite moment matrices.

We study discrete-time quantum walks on weighted graphs, where every edge in an edge cut set is assigned a small weight $\epsilon>0$. The parameter $\epsilon$ represents the strength of the connections through the cut edges: as $\epsilon \to 0$, these connections vanish, and the graph decomposes into the connected components obtained by removing the cut edges. We refer to these weighted cut edges as weak edges. We show that, for sufficiently small $\epsilon$ and on the time scale $t=\Theta(\epsilon^{-1/2})$, the finding probabilities between the connected components are asymptotically described by a continuous-time wave equation on a reduced graph, whose vertices represent the connected components and whose edges represent the weak edges connecting them. The wave equation is governed by a symmetric weighted Laplacian determined by the reduced graph and the number of arcs contained in the components. Consequently, finding probabilities of leading-term are independent of the detailed internal structures of the components. We further show that this wave equation has the same form as Newton's equation of motion for a classical spring-mass system on the reduced graph.

We study the limit shape of the range of the random walk excited to the center on $\mathbb Z^d$, with $d\geq2$. A cookie is placed at each nonzero vertex. On its first visit to such a vertex, the walker consumes the cookie and takes its next nearest-neighbor step with a bias toward the origin. On a visit to the origin, or on later visits to a nonzero vertex, no cookie is available and the walker moves to a neighbor uniformly at random. We prove that the set of vertices visited up to time $n$, rescaled by $n^{-1/(d+1)}$, converges in probability in Hausdorff distance to an explicit $\ell^1$ ball. This answers a question raised by Kozma (2007).

We study two physically distinct steady free-boundary problems in a two-dimensional inviscid fluid: a hollow vortex in a constant-vorticity flow subject to simple shear, third order and linear strain at infinity, without surface tension, and an irrotational flow past a constant-pressure bubble subject to surface tension, linear strain, and circulation at infinity. Building on the mathematical vortex-bubble correspondence recently developed by Crowdy and Tanveer, we show that both problems are linked by a common mathematical formulation. For the vortex problem, we extend the sequence-space fixed-point approach of Crowdy and Tanveer to obtain new local existence, uniqueness, and analyticity results. For the bubble problem, we develop a separate existence theory, reducing it to a nonlinear singular integral operator fixed-point problem and deriving a scalar solvability condition that defines a realanalytic surface in the physical parameter space. On this surface we obtain locally unique bubble solutions with real-analytic boundaries and holomorphically extendible velocity fields. Finally, we prove that the scalar solvability condition is equivalent to a functional conformal mapping identity. The scalar condition between the parameters is enough for the vortex and bubble problems to have the same free-boundary shape, despite their different exterior flows.

We present a one-dimensional classical statistical physics model on an infinite lattice with nearest-neighbor interactions and local state space $\mathbb{Z}^2$, with a “helical" symmetry group $\mathbb{Z}^2\rtimes \mathbb{Z}$ mixing flavor symmetry with spatial translation. For any $0<\beta<\infty$, we construct an uncountable infinity of DLR (Gibbs) states parameterized by $\mathbb{R}^2$, with a free $\mathbb{Z}^2$ flavor symmetry group action; as such, we interpret the model as exhibiting spontaneous symmetry breaking at any temperature. The most general DLR state we construct is interpreted as an infinite sequence of localized domain walls separating a pair of asymptotic “symmetry sectors". Although any normalizable Gibbs state necessarily breaks a countably infinite freely-acting symmetry group, a natural regularization of the problem to (arbitrarily) large but finite systems with periodic boundary conditions has measure concentration in disjoint and far-separated symmetry-related clusters in the (now unique) Gibbs state, which justifies our interpretation of spontaneous symmetry breaking on the infinite line. A modification of the model with local state space $\mathbb{R}^2$ must break a continuous helical symmetry at any temperature. This is not a contradiction with the Mermin-Wagner Theorem, because this continuous helical symmetry is non-compact and does not commute with translation.

The basic hypergeometric series ${}_{n+1}\phi_{n}$ whose upper and lower parameters are non-negative integer powers of $q$ satisfying a certain constraint can be, after a normalisation, computed as a positive polynomial. We derive three formulas for this polynomial. The first formula is a generalisation of the MacMahon identity in which an infinite binomial series is identified with a normalised generating function of des and maj statistics of multiset permutations. The second formula is a generating function of multiset permutations for the inversion statistic and a generalisation of the statistic mstc. The third formula is a finite sum containing $2n$ $q$-binomial coefficients.

Consider a finite planar graph with positive real edge weights and designated boundary vertices, called nodes. Such a graph is called a circular planar electrical network. A grove is a spanning forest in which every component contains at least one node. The connected components of a grove determine a partition of the nodes. We relate weighted grove counts to invariant theory for the symplectic group. To a planar electrical network $G$, we associate an $\mathrm{Sp}(2n)$-invariant tensor $Z_G$. For $\mathrm{Sp}(2)=\mathrm{SL}(2)$, we expand $Z_G$ in the Temperley–Lieb basis indexed by noncrossing matchings and relate its coefficients to the Kenyon–Wilson grove formulas. For $\mathrm{Sp}(4)$, we give reduction rules for superpositions of two groves and prove that the tensors indexed by $3$-noncrossing matchings form a basis of the space of $\mathrm{Sp}(4)$-invariant tensors. The coefficients of $Z_G$ in this basis are weighted counts of reduced double groves, up to normalization.

In this paper, we show that the height function of the six-vertex model in simply connected domains with piecewise constant boundary conditions converges to the Gaussian Free Field (GFF) with Dirichlet boundary conditions. This implies the conformal invariance of the scaling limit of the model. The argument relies on the full plane GFF convergence combined with Reflexion Positivity and qualitative estimates. The proof works for a wide range of spectral parameters $\Delta$ (among which $\Delta$ close to $0$, and between $-1$ and $-1/2$) making this paper the first instance of a conformal invariance result for a continuum of models. The paper has consequences for other models, including the FK percolation with cluster-weight $q=4$ and the Ashkin-Teller model, which we will pursue in future work.

High-subsonic turbulent jets trap acoustic modes in their potential core. The modes lie in narrow frequency bands that are $O(0.1)$-wide in Strouhal number, $St$. By studying a Mach 0.9, Reynolds number $10^6$ jet, this work confirms an earlier hypothesis: each band is made up of $O(10)$ discrete frequencies, $\Delta St \sim O(0.01)$ apart. To resolve them, we collect $O(100\,000)$ snapshots from dedicated schlieren experiments and large-eddy simulations (LES), and apply spectral proper orthogonal decomposition (SPOD). Our SPOD algorithm uses sine tapers and enforces the jet's rotational and reflectional symmetries. For both the schlieren and the LES, the trapped SPOD modes are bounded in the $St$-$x$ and $St$-$k$ planes, where $x$ and $k$ are respectively the axial coordinate and wavenumber. The bounds quantise the modes in $St$, $x$, and $k$, such that the $n_x$th mode in $St$ has $n_x$ antinodes along $x$ and $k$. We then predict trapped modes with local, global, modal, and non-modal stability theories. We find evidence of a competition between modal and non-modal stability. From only the theoretical bounds, we build a simple in-phase standing-wave resonance model that predicts the quantised global-mode frequencies.

We analyze the level lines of the Gaussian Free Field with logarithmic singularities in polygonal domains. We focus on the (none-zero) singular case and compare it to the singular-free setting. The law of the level lines for the field in singular case is absolutely continuous with respect to the law for the singular-free case, with a Radon-Nikodym derivative related to the reduced Green's energy which is introduced by F. Viklund and D. W. Nyström~[VN24]. These level lines admit a Brownian motion representation. In the singular-free case, such representation involves Poisson point processes of Brownian loops and excursions; while for the singular case, it additionally includes Poisson point processes of Brownian bubbles and bridges. The special cases of one or two singularities yield moment-generating functions of the conformal radius, which can be interpreted as one-point and two-point correlation functions of vertex operators in conformal field theory at the free-boson point. While the Radon-Nikodym derivative is bounded away from the singularities, the behavior of the level lines near the singularities is markedly different from the singular-free case, with different asymptotic probabilities for all level lines to remain close to the singularity.

In this note, we establish quantitative stability of aggregation-diffusion energy for compactly supported data. Our consideration focuses on the degenerate diffusion with local attraction that are asymptotically flat at infinity, such as Riesz kernels. We characterize the spectrum lower-bound of the Wasserstein Hessian at steady states. Assumptions are kept as minimal as that needed for uniqueness.

We study a representative two-loop family of worldline quantum field theory integrals relevant for classical gravitational scattering with a massive mediator and investigate the geometric structure of its maximal cut. We find that, unlike the massless case, the massive loops already give rise to an elliptic maximal cut at two loops, which degenerates into a nodal curve in the massless limit and in the static limit. In the global Baikov representation, two successive integrations reduce the maximal cut to a period of an elliptic curve. We further establish five primary consequences of this study: (a) The integration-by-parts method generates five master integrals, which, under reflection, split into a three-dimensional elliptic block and a two-dimensional polylog block. We derive the differential equation in two ways, one by Laporta reduction and subsequently by intersection theory in two cocycle bases, and construct the rational map between them. (b) The period matrices in arbitrary dimension have been computed in terms of Appell and Beta functions. Furthermore, we derive twisted Riemann period relations that yield nine quadratic identities among them. (c) We study the global monodromy relation of the differential system that satisfies Riemann's bilinear relation. (d) We explicitly derive the function space of the iterated integrals in terms of elliptic multiple polylogs. (e) In impact-parameter space, the Fourier-transformed cut is a Bessel-twisted differential on the elliptic curve, which we show has extra involution symmetries. Thus, the parity of the differential further decides which quotient - rational or elliptic its periods live on. All results presented concern the maximal cut and, therefore, the homogeneous solutions, but they open an important pathway to tackling the full massive two-loop integral.

In this work, we revisit the analytical structure of the classical affine Lie bialgebra underlying the integrable structures of AdS/CFT worldsheet scattering and the one-dimensional Hubbard model. Earlier work showed that the algebraic relations implied two singularity locations in the evaluation parameter plane besides the common expansion points infinity and zero for Laurent polynomials forming the basis for loop and affine algebras. Our aim is to formulate these singularities rigorously using meromorphic functions rather than by expansion into geometric series. We thus carefully analyse the analytical structure of the affine bialgebra relations in the complex plane paying attention to potential restrictions and extensions due to the additional singularities. As a first attempt with some shortcomings, we reformulate the affine bialgebra relations with the extra singularities serving as the expansion points for Laurent polynomials. We finally overcome the remaining issues by proposing three-point and four-point affine algebras for the rational and trigonometric cases. With a suitable choice of basis for meromorphic functions on the Riemann sphere with several punctures based on Krichever-Novikov algebras, we show that the multi-point affine algebras form consistent quasi-triangular Lie bialgebras.

We study magnets composed of molecules with atoms interacting via $SU(N)$-invariant two-body interactions. Atoms carry states transforming in generically different irreducible representations of $SU(N)$, and the interaction strength between atoms depends on the specific atoms involved. We derive the thermodynamics of these magnets in the mean-field approach, and find that they can exhibit mixed ferro-antiferromagnetic behavior. We present a full analysis of the simplest nontrivial case of molecules consisting of two atoms in the spin-$j$ representation of $SU(2)$, which generalizes conventional magnetic systems, and derive its phase structure and transitions.

Building on the recently established de Sitter (dS)-covariant indecomposable Krein realization of the scalar discrete-series unitary irreducible representations $\Pi_{p,0}$, $p=1,2,\cdots$, of $\mathrm{SO}_0(1,4)$, naturally organized into a Gupta-Bleuler triplet, we uncover its underlying Araki-cohomological structure. We show that the Krein-Gupta-Bleuler construction provides a concrete realization of Araki's standard Gupta-Bleuler triplet, with its non-split indecomposable structure encoded by non-trivial first cohomology classes related by adjunction. We further show that the reducible intermediate sector naturally resolves into its two irreducible components, inducing a corresponding decomposition of the extension classes and yielding a four-layer refinement of Araki's standard triplet. The resulting Gupta-Bleuler quadruplet provides a finer cohomological resolution, distinguishing the physical representation from its complex-conjugate sector.

Large explosive eruptions and earthquakes excite atmospheric oscillations near 3.7 and 4.4\,mHz that couple to the solid Earth. For vertically propagating linear acoustic–gravity waves in a hydrostatic ideal-gas atmosphere, the travel-time formulation gives a Klein–Gordon equation with a potential $Q(\tau)$. We establish three main results. First, for every potential admitting a positive zero-energy solution, the corresponding atmospheric profiles are constructed explicitly by quadrature; this extends the known reflectionless profiles of constant $Q$. Second, Darboux–Crum potentials give a smooth atmosphere that reproduces the U.S. Standard Atmosphere between 11 and 100\,km to within 3\,K and is exactly transparent to vertical waves above its cut-off; it supports no damped overtone near 4.4\,mHz, and its ground-confined mode below the cut-off is perfectly trapped. The observed spectrum therefore requires a cut-off barrier of finite thickness connecting the lower atmosphere to the thermosphere. Third, a Rosen–Morse barrier gives an exactly solvable atmosphere with a closed-form hypergeometric resonance condition. Its resonances at 3.76 and 4.37\,mHz, with leakage quality factors 173 and 20, explain the different damping of the two oscillations: the fundamental lies below the top of the mesospheric cut-off barrier and leaks by tunnelling, whereas the overtone lies above it. Full-wave computations for event-specific atmospheres reproduce the reported 3.7–3.8\,mHz fundamental oscillation in all six events, of seven considered, in which such a mode was identified.

The measures of distance frequently used in quantum information, such as trace distance or fidelity-based purified distance, are the smallest extensions of the corresponding distance measures in classical information theory. However, this way of extending classical distances is not unique, and a whole spectrum of other extensions can be defined. Here we study the question of how quantum information processing tasks are affected by a change of the error metrics to the maximal extensions of the classical distance measures, imposing more demanding error requirements on operational tasks. We find that the performance of some tasks, such as channel coding or quantum resource distillation, is not affected whatsoever by this change. However, for other tasks such as channel simulation and quantum resource dilution, we show that the rates are now given not by functions of the standard (Umegaki) quantum relative entropy, but ones based on the Belavkin-Staszewski relative entropy. Our results connect the Belavkin-Staszewski relative entropy with operational tasks and reveal that known reversibility results in quantum information, including the reverse Shannon theorem and the asymptotic reversibility of quantum resource transformations, no longer hold under maximal distance measures.

We determine the two-way quantum, entanglement-distribution, private, and secret-key capacities of the pure-loss bosonic channel under an unconditional mean transmitted-photon-number constraint. For transmissivity $\eta$ and mean photon number $N$, all four capacities coincide and are given by $g(N)-g((1-\eta)N)$, where $g$ is the entropy of a thermal mode. This resolves the longstanding energy-constrained capacity problem by establishing the optimality of the reverse-coherent-information rate introduced in 2009. Our central tool is sector teleportation simulation, which we develop specifically to transfer the input-energy constraint to the shared entanglement resource, thereby preserving the constraint throughout converse arguments for general adaptive protocols. For every $N>0$, we further show that the corresponding strong-converse thresholds coincide with the unconstrained value $-\log_2(1-\eta)$. For parallel protocols with a hard total-photon-number cutoff, the same energy-constrained capacity formula instead satisfies an exponential strong converse. As an extension, we determine the energy-constrained two-way capacities of the quantum-limited amplifier, showing that classical assistance does not improve its unassisted quantum and private rates. Together, these results establish a unified finite-energy framework for adaptive bosonic communication and reveal how energy constraints fundamentally reshape both attainable rates and converse bounds.

We study agnostic tomography of pure bosonic Gaussian states: given copies of an arbitrary $n$-mode bosonic state $\rho$, the goal is to output a pure Gaussian state whose infidelity with $\rho$ is at most $\mathrm{opt} + \epsilon$, where $\mathrm{opt}$ is the minimum infidelity achievable by any pure Gaussian state. We give efficient protocols achieving this in both the high and low fidelity regimes. When $\mathrm{opt}$ is below some universal constant, our protocol has runtime and copy complexity which is strongly polynomial in $n, 1/\epsilon$ and $\log \log E$, where $E$ is the energy of the closest pure Gaussian state. For arbitrary $\mathrm{opt}$, our protocol uses $(n+1)^{\mathrm{poly}(1/\epsilon)} \mathrm{poly}\left(1+\log\log(E)\right)$ copies and runtime. As a corollary, we obtain the first truly tolerant Gaussianity testing protocol for distinguishing whether $\mathrm{opt} > c + \epsilon$ or $\mathrm{opt} < c - \epsilon$, for any threshold $c\in(0,1)$. We also prove $\mathrm{poly}(n,1/\epsilon)$ runtime is impossible, unless $\mathrm{NP}\subseteq\mathrm{BQP}$. Our protocols follow a shared paradigm: first, we iteratively use general Gaussian measurements combined with techniques from classical robust statistics to obtain a good warm start estimate, then we leverage non-Gaussian measurements to refine this warm start using convex and non-convex optimization methods. Interestingly, we prove that non-Gaussian measurements are necessary to match the strong agnostic guarantees we obtain, and in fact these guarantees are provably superior to what is possible for robustly estimating classical Gaussians.

The Sachdev-Ye-Kitaev model is a strongly interacting fermionic system that has been well-studied in condensed matter and high energy physics. It is highly quantum: Gaussian states are far from the thermal state (Hastings and O'Donnell, STOC'22) and representing the thermal state requires large polynomial-size quantum circuits (Anschuetz et al., QIP'25). Very recently, it was nonetheless proven that classical algorithms can estimate local thermal expectations at sufficiently high temperature in quasipolynomial time (Zlokapa, FOCS'26). We show that classical algorithms can in fact estimate local observables at all constant temperatures in polynomial time. Our techniques also extend straightforwardly to classical systems: we resolve an open question about computing thermal expectations of a classical spin glass up to its phase transition (Bencs et al., STOC'26). Our proof develops a fully rigorous quantum cavity method. Due to the success of the classical cavity method in optimization, sampling, inference and learning, we expect the quantum cavity method to find further applications of independent interest. As an example, we give a quantum algorithm that learns SYK Hamiltonians from the Gibbs state at any constant temperature with polynomial time and sample complexity.

In a previous work, we showed that real quantum theory (RQT) cannot be experimentally distinguished from ordinary quantum theory (QT). In this paper, we investigate whether this indistinguishability survives two natural extensions of the setting: allowing separated measurements to be represented by commuting rather than tensor-product observables, and imposing superselection rules, as in fermionic information theory. We show that it does in both cases. Our first result is a positive answer to the Tsirelson problem in RQT: commuting and tensor-product measurements generate the same finite-dimensional correlations. This is surprisingly not a trivial consequence of the standard complex proof, as it does not carry over to the reals. The proof obstruction becomes particularly relevant in the presence of superselection rules, which is why we first establish the equivalence in RQT before extending the framework to superselected RQT. Our second result is a local, real quantum formulation of superselected theories. We extend the RQT framework to accommodate a representation of superselection over the reals and show, in particular, that it admits a fermionic version whose predictions are experimentally indistinguishable from those of fermionic information theory. More generally, the construction extends to all superselected QTs.

We derive rates of exponential relative-entropy decay for a broad class of infinite-dimensional quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined quantum Coulomb gases and molecular systems, we prove exponential entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time $L^2$-to-$L^p$ bound for any $p>2$.

Self-testing certifies quantum states and measurements from observed correlations alone, without requiring a description of the devices that produce them. In this work we establish, to the best of our knowledge, the first robust self-test of the full continuous family of measurements generated by Majorana operators. We achieve this by showing that the Grothendieck game, a two-player nonlocal game in which the players receive directions on a sphere and return binary answers, is a self-test of Majorana observables. That is, any near-optimal performance certifies an entire continuously parameterized family of quantum measurements. We further extend this certification to products of Majorana observables, obtaining a robust self-test of the spin representation of the continuous pin group.

We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate $k$-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.

We completely determine the possible parities of the Euler characteristic of closed $Pin^{\pm}$-manifolds of a given dimension. As an application we partially calculate the controlled cut-and-paste groups $SKK_{2k+1}^{Pin^{\pm}}$, which were previously undetermined.