Frequency modes of light are one of the most promising platforms that provide access to high-dimensional quantum states amongst different photonic degrees of freedom capable of high-dimensionality, enabling robust, error-tolerant, and scalable quantum optical information systems. We demonstrate engineering of precisely controlled two-photon high-dimensional states entangled in frequency through time-domain Fourier optical synthesis. We generate and convert a continuous broadband frequency-entangled state into a large range of discrete frequency bins suitable for ITU standards, with spacings ranging from 12.5 GHz to 750 GHz, and observe spectral anticorrelations over 38 frequency bins, including intra-bin pure states at a 100 GHz bin spacing. We characterize the full quantum state dimensionality via Schmidt decomposition and observe lower bounds on the frequency-binned Hilbert-space dimensionalities of at least 289, formed by two entangled qudits with dimension 17. Furthermore, we demonstrate quantum nonlocality via frequency correlations in a transmission experiment over a campus-scale two-node fiber network. This work represents a crucial step towards building a versatile and relatively simple way of generating precisely controlled high-dimensional spectral qudits, with the potential of harnessing in wavelength-multiplexed quantum networks, high-dimensional information processing, and communication of quantum states specifically, and fiber-optic quantum remote sensing.

We present a multi-wavelength physical characterization of 14 luminous Ly$α$ emitters (LAEs) at $z\approx6$, integrating deep ground-based Magellan/M2FS spectroscopy with heterogeneous JWST/NIRCam broad- and medium-band imaging. Identified via strong Ly$α$ lines with extreme Ly$α$ luminosities of ${>}10^{42.6}$ erg s$^{-1}$, the sample exhibits very large rest-frame equivalent widths (${\gtrsim}100$ Å) and steeply blue UV continua ($β_{\rm median}\simeq-2.2$, $-18.2>M_{\rm 1500}>-20.2$ mag). Crucially, the integration of NIRCam medium-band photometry (F410M) breaks the degeneracy between strong rest-optical nebular emission and Balmer breaks, resolving prior mass overestimations. The tightly constrained spectral energy distribution modeling demonstrates that these luminous LAEs tend to be unequivocally low-mass, ultra-young dwarf starbursts; half the sample is characterized by stellar masses of $M_* < 10^8 M_{\odot}$, ages $\lesssim10$ Myr, and negligible dust attenuation. We also map the production efficiency of ionizing photons and Ly$α$ escape fractions ($f_{\rm esc}^{\rm Lyα}$). The $f_{\rm esc}^{\rm Lyα}$ values are exceptionally high, with a median of ${\gtrsim}40$%, increasing for the bluer UV continua. Finally, analyzing spatial offsets between the Ly$α$ centroid and the stellar counterpart, we demonstrate empirically that internal dust content, rather than neutral hydrogen gas, dominate the suppression of Ly$α$ radiative transfer. Our study reveals that strong Ly$α$ emission of the luminous LAEs are generally attributed to both the vigorous starburst activities and the high $f_{\rm esc}^{\rm Lyα}$. Resembling Lyman continuum leakers, these extreme dwarf systems function as highly efficient ionizing engines at the conclusion of the Epoch of Reionization.

The growing adoption of AI agents and the Model Context Protocol (MCP) has motivated organizations to expose existing REST APIs as agent-consumable tools. In our industrial context, this initiative targeted an ecosystem of 16 production APIs comprising approximately 600 endpoints. Although these APIs were stable and widely used within a microservice architecture, early proof-of-concept experiments revealed systematic failures in task planning, tool selection, and payload construction when accessed through MCP-based agents. Rather than attributing these failures to model limitations alone, we conducted an ecosystem-scale empirical assessment of the underlying OpenAPI documentation. We developed Hermes, a multi-agent LLM-based system that detects documentation and REST-related smells at the endpoint level and generates explainable diagnostic reports. The large-scale evaluation identified 2,450 smells across 600 endpoints, with deficiencies present in all analyzed operations. Practitioner validation confirmed high agreement with the detected issues while also revealing contextual trade-offs in remediation decisions. The findings suggested that structural validity within microservice environments does not guarantee semantic readiness for agent-based consumption. Based on this evidence, the organization revised its adoption strategy, prioritizing selective endpoint adaptation, redefining documentation standards, and integrating automated documentation assessment into API governance workflows. This case illustrates how systematic artifact-level evaluation can function as a strategic decision-support mechanism, reducing technological risk and guiding evidence-based AI adoption in industrial software ecosystems.

The Sagittarius (Sgr) Stream is produced by the ongoing disruption of the Sgr dwarf spheroidal (dSph) galaxy and is thought to contain multiple wraps that were stripped during different pericentric passages. In this study, we introduce a neural-network--based method trained on $N$-body simulations to infer the stripping time of Sgr Stream stars directly from their phase-space coordinates. We combine spectroscopic data from SEGUE, APOGEE DR17, and LAMOST DR7 LRS with \textit{Gaia} EDR3 astrometry and distance estimates from the latest \texttt{StarHorse} catalog to identify high-quality Sgr Stream members. Applying our method to these stars, we measure a clear metallicity gradient with stripping time, well described by a linear relation with slope $\sim 0.3~\mathrm{dex~Gyr^{-1}}$. We further predict the stripping times of globular clusters previously suggested to originate from the Sgr dSph. M 54, Terzan 7, Terzan 8, and Arp 2 exhibit stripping times consistent with being currently bound to the Sgr remnant. Pal 12, Whiting 1, and NGC 2419 are inferred to have been stripped $0.9 \pm 0.1$, $1.1 \pm 0.2$, and $2.1 \pm 0.2$ Gyr ago, respectively. For NGC 4147 and NGC 5634, whose membership in the Sgr system remains uncertain, our analysis suggests stripping times of $1.1 \pm 0.4$ and $1.1 \pm 0.1$ Gyr, respectively, if they are ultimately confirmed as genuine Sgr members. These results demonstrate that data-driven models of dynamical stripping histories offer a promising approach for reconstructing the formation and chemical evolution of the Sgr Stream.

As large language models reshape scientific research, literature retrieval faces a twofold challenge: ensuring source authenticity while maintaining a deep comprehension of academic search intents. While reliable, traditional keyword-centric search fails to capture complex research intents. Frontier LLMs can handle complex research intents, but their high cost and tendency to hallucinate remain key limitations. Here we introduce PaSaMaster, a self-evolving agentic literature retrieval system that produces relevance-scored paper rankings with evidence-grounded recommendations through iterative intent analysis, retrieval, and ranking. It is built on three key designs. First, it transforms literature retrieval from a one shot query--document matching problem into a search process that evolves over time, using ranked evidence to reveal gaps, refine intents, and guide follow-up searches. Second, it prevents hallucinated sources by treating retrieval as intent--paper relevance ranking rather than generation. Finally, PaSaMaster improves cost efficiency by separating planning from retrieval: a frontier LLM is used only for intent understanding, while large scale retrieval and relevance scoring are delegated to customized corpora and lightweight models. Evaluated on the PaSaMaster Benchmark across 38 scientific disciplines, our system exposes the severe inaccuracy and incompleteness of traditional keyword retrieval (improving F1-score by 15.6X) and the unreliability of generative LLMs (which exhibit hallucination rates up to 37.79%). Remarkably, PaSaMaster outperforms GPT-5.2 by 30.0% at a mere 1% of the computational cost while ensuring zero source hallucination: https://github.com/sjtu-sai-agents/PaSaMaster

Two-dimensional (2D) van der Waals (vdW) multiferroics offer an attractive platform for four-state nonvolatile memory by combining switchable ferroelectric polarization and magnetization within a single material system. However, their development is hindered by the scarcity of synthesizable candidates and the lack of non-destructive readout schemes. Here, we combine machine-learning screening with first-principles calculations to explore the 2D vdW ABC$_2$X$_6$ family and identify a set of high-confidence multiferroic candidates. Among them, AuCrP$_2$S$_6$ monolayer emerges as a representative system with a ferromagnetic ground state, a sizable out-of-plane polarization of 7.46 pC/m, and a moderate ferroelectric switching barrier of $\sim$130 meV/f.u. Moreover, the nonlinear optical response mediated by the bulk photovoltaic effect (BPVE) in AuCrP$_2$S$_6$ provides a dual-channel probe of the ferroic orders, in which the polarization direction governs the photocurrent sign while the magnetic order selects the spin channel via robust exchange splitting. This intrinsic coupling enables the non-destructive readout of four logic states within a single atomic layer, thereby providing a practical blueprint for next-generation multistate optoelectronic memory.

We study monotone Hermite interpolation on an interval, where both function values and first derivatives are prescribed at the nodes. Among all $C^{1,1}$ interpolants, we seek one with optimal curvature, measured by $\|F''\|_{L^\infty}$. In this paper, we analyze the limitations of some classical techniques, and provide an explicit optimal construction in $C^{1,1}$ given by quadratic splines by studying the optimal velocity profile. Moreover, given $E = \{x_1,\cdots,x_N\}$ and $f: E\to \mathbb{R}$ (without derivatives), we also provide a formula to compute the corresponding trace seminorm \[ \inf\Bigl\{ \|F''\|_{L^\infty} : F(x)=f(x) \text{ on $E$ and } F'\ge 0 \text{ everywhere} \Bigr\}. \] In addition, we also describe how to mollify $C^{1,1}$ solutions to $C^2$ while preserving monotonicity and sacrificing a controlled amount of optimality.

This letter investigates the problem of energy efficient collaborative strategy for mobile embodied artificial intelligence network (MEAN) over wireless communication. In the considered model, the agents execute the tasks through collaboration, and they can switch between two operating modes based on the signal-to-noise ratio (SNR) and global collaboration. The dual-mode comprises the base station (BS)-assisted collaborative mode, in which agents make decisions through semantic communication with BS and then collaborate on tasks, and the local computing mode, in which the agents make decisions and execute tasks independently. Due to the dynamic wireless communication and flexible collaboration strategy, we jointly consider computation energy, communication energy, and task-execution energy with specific collaborative gains into a mixed-integer nonlinear programming (MINLP) optimization problem whose goal is to minimize the total system energy consumption. To solve it, we propose a lower-complexity enumeration algorithm: first, we get the optimal closed-form solution for semantic compression ratio and transmit power by proving the strict convexity. Second, we determine the scale of collaboration and the operating mode of each agent by a greedy sorting algorithm based on individual energy-saving potentials. Simulation results show that the proposed algorithm can significantly reduce the total energy consumption compared to benchmark schemes.

Complex numbers play an indispensable role in quantum mechanics and quantum information, as validated by both theoretical analysis and experimental verification. Since quantum information processing inherently relies on quantum channels, the resource theory for quantum channels is equally fundamental to that for quantum states. In this paper, we propose two frameworks for quantifying the imaginarity of Gaussian channels. The first framework regards all real superchannels as free superchannels. Within this setting, we introduce two concrete imaginarity measures for Gaussian channels: I_s^GC based on existing imaginarity measures of Gaussian states, and I_d^GC derived directly from the intrinsic parameters of Gaussian channels, which enjoys high computational simplicity. The second framework adopts only a proper subset of real superchannels as free superchannels. Under this framework, we put forward another imaginarity measure I_c^GC , which is fully determined by the inherent parameters of Gaussian channels and features continuity as well as tractable computation. As a practical application, we employ I_c^GC to investigate the dynamical behavior of Quantum Brownian Motion Gaussian channels throughout the entire evolutionary process.

For a multi-user multiple-input multiple-output (MU-MIMO) wireless communication system, imagining that the locations of the users are now fully controllable, what is the maximum sum-capacity, and what are the corresponding optimal user locations? While these questions are irrelevant in conventional human-centric communications with random user mobility, they become critically important for emerging applications involving ground or aerial robots. This paper addresses these fundamental questions in the context of MU-MIMO communications with an unmanned aerial vehicle (UAV) swarm acting as the users. To this end, we first derive closed-form expressions for the sum-capacity of MU-MIMO UAV swarm communications. Our results reveal that, compared to conventional MU-MIMO systems, the additional degrees of freedom provided by the coordinated mobility of the UAV swarm yields substantial capacity enhancement. Specifically, when the base station (BS) is equipped with an $M$-element uniform linear array (ULA), the full spatial multiplexing gain and beamforming gain, both equal to $M$, can be achieved simultaneously. For a BS with a uniform planar array (UPA), we show that asymptotically $\frac{πM}{4}$ users can simultaneously enjoy the full beamforming gain $M$. Furthermore, we propose a novel framework to optimize UAV swarm formation for maximizing the sum-capacity achieved by successive interference cancellation (SIC) and maximizing the sum-rate via treating interference as noise (TIN), taking into account practical considerations such as collision avoidance and swarm cohesion constraints. By exploiting the manifold structure of the array response vectors with respect to UAV directions, we develop an efficient algorithm to solve the resulting non-convex formation optimization problems. Extensive simulation results demonstrate that the proposed algorithms achieve near-optimal performance.

We study random order semi-streaming algorithms for submodular maximization under a wide range of combinatorial constraint classes, including matroids, matroid $p$-parity, $p$-exchange systems and $p$-systems. For most of these classes of constraints, our results are the first improvement over what is known to be achievable for adversarial order. For matroids, matching and $p$-matchoids, previous random order results were known, and we improve over some of these as well. In the case of matroids, our improved results show a separation between adversarial and random order semi-streaming algorithms, and exponentially improve the number of passes necessary for getting $1 - 1/e - \varepsilon$ approximation for maximizing a monotone submodular function subject to a matroid constraint. We also prove a new hardness result showing a similar separation for $p$-systems. Our results are based on two new technical tools. One tool provides a general way to translate offline algorithms for many classes of constraints into random order semi-streaming algorithms. The other tool is a semi-streaming variant of a recently proposed offline algorithm for matroid constraints.

Periodically driven quantum many-body systems can spontaneously break discrete time-translation symmetry, realizing discrete time crystals. To date, both experimental and theoretical efforts have largely focused on the simplest case of spontaneous period-doubling in $\mathbb{Z}_2$ discrete time crystals realized with qubits. This owes, in part, to the challenge of stabilizing eigenstate order in higher discrete symmetry ($\mathbb{Z}_n$) time crystals, due to the presence of richer domain wall physics. Here, we demonstrate the realization of a $\mathbb{Z}_3$ discrete time crystal by implementing a Floquet chiral clock model in a chain of 15 superconducting qutrits. Unlike the conventional Ising setting, our system features a tunable chiral angle that governs domain-wall dynamics, spectral degeneracies, and crucially, the stability of time-crystalline order. Using disordered nearest-neighbor chiral interactions, we observe robust subharmonic period tripling that persists across a wide range of drive strengths and is independent of initial state. Finally, we highlight the special role that chirality plays in our $\mathbb{Z}_3$ discrete time crystal -- in its absence, the system's Floquet dynamics exhibit a marked initial state dependence governed by domain wall degeneracies. Our results establish native qudit hardware as a powerful platform to access a broader landscape of non-equilibrium phases.

Recent interest in applying machine learning methods to predict invariants of mathematical objects has yielded models with surprisingly strong performance, including those predicting traces of Frobenius for elliptic curves. We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions. To ensure future models capture new arithmetic properties rather than potentially exploiting these dataset artifacts, we introduce a benchmark dataset consisting exclusively of unique twist class representatives.

Conical intersections play central roles in photoinduced reactions. However, comprehensive conical-intersection datasets that could advance our understanding of excited-state reaction processes remain scarce. To address this gap, we constructed a quantum chemistry dataset containing ground-state and conical-intersection structures of small molecules (up to ten heavy atoms: C, N, O, F). Ground-state geometries were optimized at the semi-empirical OM2 level, with single-point energies calculated at the OM2/MRCI level. Conical-intersection geometries and energies were also computed at the OM2/MRCI level. This dataset is designed to enable a deep integration of photochemistry with machine learning, bridging the gap between photochemical insight and data-driven approaches.

We prove mixed-characteristic analogues of the Connes and Feigin--Tsygan degeneration theorem. Let $W=W(k)$ be the Witt vectors of a perfect field of characteristic $p>0$. For a smooth proper variety $X$ over $W$, the de Rham-to-$\HP$ spectral sequence is split degenerate under the small-dimension hypothesis $dim(X/W)<p-1$. More generally, if $X$ is smooth and proper over the ring of integers $O_K$ of a finite extension of $\mathrm{Frac}(W)$ with ramification index $e$, we prove the corresponding split degeneration under $2e dim(X/O_K)<p-1$. Under the same ramification hypothesis, we also prove split degeneration of the $Ainf$-to-$TP$ spectral sequence. Finally, after inverting an explicit factorial, we obtain a topological $q$-de Rham analogue.

This paper presents a flexible energy management system (EMS) for an electric bus charging station (EBCS) that integrates renewable generation, energy storage, and electric bus (EB) charging while accounting for uncertainties in solar PV output, electricity prices, and EB arrival/departure state of charge. A data-driven polynomial chaos expansion surrogate is developed from a limited set of uncertainty samples, and a nonparametric inference method is used to enrich the input data when historical data is limited. Case studies on a solar-powered EBCS with 20 EBs demonstrate the effectiveness of the proposed EMS and data-driven method.

Atom interferometers represent a promising approach for gravitational wave detection in the decihertz frequency band, complementary to existing light-based detectors. The South Pole offers unique advantages for such experiments: exceptionally low seismic noise, established infrastructure for large scientific projects, and a location that strengthens gravitational wave source localization through global triangulation. Here we discuss the scientific case and practical considerations for deploying a long-baseline atom interferometer at the South Pole, which has the potential to expand the global network of gravitational wave detectors while enabling precision tests of fundamental physics.

Long-term outcomes are often unavailable in randomized clinical trials, although short-term surrogate outcomes are commonly observed. External observational data may contain the long-term outcome, but causal comparisons based on such data alone are vulnerable to confounding. Existing surrogate-based data integration methods for long-term outcomes have focused primarily on average treatment effects. We study estimation of quantile treatment effects for long-term outcomes in the trial population by combining randomized trial data with external observational data. Under treatment randomization, positivity, and a surrogate-based transportability assumption, we establish identification and develop a doubly robust estimator for inference. The estimator accommodates flexible machine learning methods for nuisance estimation, remains consistent if either the score-related or outcome regression-related nuisance functions are consistently estimated, and is asymptotically normal under regularity conditions. Simulation and real-data results demonstrate that the proposed method performs well in finite samples and can reveal heterogeneous long-term treatment effects across quantiles.

We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the optimal value. However, the lower bound thus obtained is not exact in general due to the lack of strong duality. In this paper, we propose a generalized dual decomposition (GDD) that extends the linear regularizer used in dual decomposition to a general nonlinear one, which still admits parallelization while exhibiting strong duality. By encoding the nonlinear regularizers through parameterization and cutting planes, we establish the convergence of a GDD algorithm to achieve global optimum. In addition, we discuss strategies for solving the GDD scenario subproblems more efficiently, including pruning and valid inequalities. Furthermore, we extend GDD to a more general, constrained form that subsumes, as special cases, robust optimization, chance-constrained programs, and bilevel optimization with multiple followers. Finally, numerical experiments demonstrate the strong duality of GDD, its computational efficacy versus primal (Benders-type) decomposition algorithms, and the speedup through parallel computing.

Physical layer security (PLS) is a promising paradigm for safeguarding 6G wireless networks by exploiting the inherent characteristics of wireless channels. However, the efficiency of conventional PLS is often limited by fixed orientation antennas. This paper investigates a rotatable antenna (RA)-aided secure multiple-input multiple-output (MIMO) communication system, where both the transmitter and the receiver are equipped with RAs in the presence of an eavesdropper. By dynamically optimizing the orientations of RAs, we can proactively reshape the effective MIMO channels to enhance legitimate transmission while simultaneously suppressing information leakage to the eavesdropper. We formulate a secrecy rate maximization problem by jointly optimizing the transmit beamforming, artificial noise (AN) covariance matrix, and the transmit/receive RA orientations, subject to the transmit power budget and antenna orientation constraints. To tackle the resulting highly coupled and non-convex problem, we first study a simplified single-input single-output (SISO) case to reveal the structure of the optimal RA orientation. For the general MIMO case, we develop an alternating optimization algorithm by reformulating the original problem through the minimum mean-square error framework. In particular, the transmit beamforming and AN covariance matrix are derived in semi-closed forms, while the RA orientations are updated via the Riemannian Frank-Wolfe method. The proposed design is further extended to the multi-receiver secure transmission scenario. Simulation results show that the proposed scheme converges rapidly and achieves significant secrecy rate gains over the conventional fixed-orientation scheme.

Photonic time crystals are electromagnetic media with periodically time-varying parameters, enabling momentum band gaps, parametric amplification, and frequency conversion beyond what is possible in time-invariant systems. So far, they have been explored mainly in single-mode systems, which limits the range of accessible physical phenomena. Here, we introduce an impenetrable metasurface waveguide as a multimode time-varying platform supporting both guided surface modes and higher-order guided volume modes. We show that temporal modulation in this platform gives rise not only to conventional intramodal band gaps associated with same-branch coupling, but also to tilted intermodal band gaps originating from coupling between different guided-mode branches. Unlike intramodal band gaps, these intermodal band gaps are not restricted to half the modulation frequency and can enable directional wave amplification, where the amplified field carries energy along the waveguide even inside the band gap. We further show that the modulation phase difference provides an effective symmetry-control parameter: by exploiting temporal glide symmetry, one can selectively suppress or enhance gap opening for interactions between modes of the same or different symmetry. These results establish a versatile multimode platform for photonic time crystals, offering one of the simplest and most experimentally accessible routes to tilted band gaps compared with volumetric dispersive PTC implementations and, more broadly, opening new opportunities for time-varying electromagnetic systems.

Ruddlesden-Popper nickelates exhibit superconductivity under pressure in bulk crystals and under epitaxial constraint in thin films, while remaining highly sensitive to sample quality, oxygen content, defects, and stress conditions. We propose that the metastable RP lattice becomes superconducting only when the local constrained deformation of the Ni-O framework falls within a bounded shear-strain window. This deformation controls octahedral rotations, the interlayer Ni-O-Ni bond angle, and coupling between Ni dz2 and dx2-y2 orbitals. This shear-stress-constrained superconductivity scenario unifies the understanding of the pressure threshold, reversibility, spatial inhomogeneity, pressure-medium dependence, film-substrate sensitivity, and reproducibility.

A recent analysis of photospheric radius expansion X-ray bursts from the low-mass X-ray binary 4U 1746-37 reported unusually small mass and radius estimates for the neutron star, suggesting it could be a quark star or quark-cluster star. Here, we propose an alternative interpretation: the star's mass and radius could be underestimated from significant blocking of the X-ray flux. Significant blocking factors ($\mathcal{B} \gtrsim 0.8$, reducing the observed flux to $\sim17\%$ of the intrinsic emission) permit neutron star parameters consistent with the canonical values: $M = 1.59 \pm 0.69 M_{\odot}$, $R = 13.0 \pm 5.45\,\mathrm{km}$, or $M = 2.12 \pm 1.08 M_{\odot}$, $R = 9.80 \pm 4.13\,\mathrm{km}$. The blocking factor, which varies with the photospheric radius, provides a natural explanation for the anomalously large peak-to-touchdown flux ratio ($\sim2.0$) and highlights the importance of accounting for geometric system configuration in neutron star mass--radius estimates.

We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong $U(1)$ symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.

We study distributed inner product estimation for $n$-qubit states using local randomized measurements, for which rigorous worst-case guarantees are less understood. We first reduce the minimax kernel optimization to Hamming-distance kernels. Within this class, unbiasedness fixes a unique kernel. For this kernel under local Clifford sampling, we prove a sharp fourth-moment bound using the single-qubit Clifford commutant. This yields worst-case sample complexity $\mathcal{O}(\sqrt{4.5^n})$, attained by identical pure product stabilizer states. For the same kernel under local Haar sampling, we prove a local twirling identity that compares its fourth moment with the Clifford fourth moment. This gives the same rigorous upper bound as in the Clifford case, but the comparison is lossy. This motivates the conjectured sharper Haar scaling $\mathcal{O}(\sqrt{3.6^n})$ attained by product states, and verify it for several important classes of states. We also show that independent single-qubit Pauli shadows have worst-case scaling $\mathcal{O}(\sqrt{7.5^n})$ for large $n$.

We investigate the structural properties of the last passage time $σ_z^λ$ at level $z > 0$ of a Brownian motion with positive drift $λ> 0$, denoted $B^λ = (B_t + λt)_{t \geq 0}$, in the filtration generated by the process $ξ^{λ,z} = (B^λ_{t \wedge σ_z^λ})_{t \geq 0}$. We compute the compensator of $σ_z^λ$ and establish that it is the unique totally inaccessible stopping time in the filtration of $ξ^{λ,z}$. Moreover, we provide a canonical decomposition of arbitrary stopping times: for any stopping time $T$, the restriction of $T$ to the set $\{T = σ_z^λ\}$ is totally inaccessible, while its restriction to $\{T \neq σ_z^λ\}$ is predictable. Although the paths of $ξ^{λ,z}$ are continuous, the process fails to satisfy the Feller property and is not strong Markov. Nevertheless, we show that its natural filtration is quasi-left-continuous. To overcome these limitations, we consider the extended process $ζ^{λ,z} = (\mathbb{I}_{\{t < σ_z^λ\}}, ξ_t^{λ,z})_{t \geq 0}$, and prove that it is a Feller process. We compute its infinitesimal generator, which allows us to characterize the associated class of martingales and identify the solutions to certain partial differential equations.

In this paper, we show that time crystals can emerge in coupled exciton-polariton condensates without periodic external driving, enabled instead by incoherent gain and dissipation channels inherent to semiconductor microcavities. We present a full quantum description of these processes that recovers the established effective theory at the mean-field level. We analytically determine the mean-field phase diagram for the time-crystalline phase and find that its emergence requires the ratio of Kerr nonlinearity to nonlinear dissipation to exceed $\sqrt{5/4}$. Within this regime, the periodic oscillation of the particle numbers forms an attractor that is insensitive to the initial conditions. Numerical bifurcation diagrams reveal transitions between the time-crystalline phase and various steady phases, in excellent agreement with the analytical results. Using Bogoliubov perturbation theory, we evaluate the leading-order quantum corrections and find that, over a wide parameter range, these corrections remain periodic and much smaller than the mean-field background, thereby establishing the robustness of the time crystal.

Spin-band splitting is a hallmark of altermagnetism, intrinsically linked to magnetic ordering driven by electron correlations. However, recent inconsistencies in the detection of altermagnetism in strongly correlated altermagnet candidates have cast doubt on the robustness of this phenomenon and its dependence on many-body effects. Here, using state-of-the-art quantum many-body frameworks, we dissect the electronic origins of altermagnetism in three prototypical candidates: MnF$_2$, MnTe, and RuO$_2$. In MnF$_2$, we identify pronounced local electron correlations within Mn-3$d$ states and uncover a distinct Mott gap in the visible range, rooted in nonlocal screening effects. The strong correlations markedly localize the Mn-3$d$ electrons, leading to a narrowing of the spin-resolved bandwidth and, consequently, a suppression of spin-band splitting. By contrast, MnTe provides an ideal platform for altermagnetism, exhibiting substantial local Mn-3$d$ magnetic moments due to the strong correlations and pronounced spin-band splitting, enabled by robust Mn 3$d$--Te-5$p$ orbital hybridization. RuO$_2$ manifests as a Pauli paramagnet with vanishing local moments, even in its antiferromagnetic phase. Nonetheless, it exhibits significant spin-band splitting, indicative of itinerant altermagnetic behavior. Our results reveal that both strong local electron correlations and judicious ligand selection to promote orbital hybridization are key prerequisites to realizing altermagnetism in strongly correlated systems. These insights pave the way for the rational design and discovery of novel altermagnetic materials.

Possible anomalous couplings of the Higgs boson to vector bosons and fermions are studied using Higgs boson candidates decaying to a pair of photons. The study is based on proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with Higgs boson candidates produced via gluon fusion, electroweak vector boson fusion and in association with a vector boson, are categorized using matrix element techniques and multivariate discriminants. The $CP$ properties of the Higgs boson couplings to gluons through loops of heavy particles, as well as the tensor structure of its interactions with two electroweak bosons, are investigated. The results are interpreted in terms of the fractional contributions of anomalous Higgs boson couplings to the total production cross section of each process and are found to be consistent with the standard model expectations.

Nitrogen-vacancy (NV) centres in diamond can be used to detect radiofrequency (RF) signals through coupling of the RF magnetic field with the NV spins, combined with optical readout of the spin state. The sensitivity of such RF detectors has so far been mainly studied in terms of magnetic field sensitivity, which is relevant when the RF signal is generated by a near-field source. However, for applications where the RF input is delivered externally, a more relevant quantity is the sensitivity in terms of the input RF power. Here we theoretically analyse the power sensitivity of NV-based RF detectors as a function of the RF-spin interface geometry. We derive scaling laws of the power sensitivity for both slope-detection and variance-detection RF sensing protocols, and for various noise regimes. We find that, in most scenarios, the power sensitivity scales inversely with the characteristic physical dimension of the RF-spin interface, for instance the width of a coplanar waveguide or the diameter of a loop antenna. In other words, the smaller the structure and the probed NV volume, the better the power sensitivity, which is contrary to the case of magnetic field sensitivity. Lastly, we numerically estimate that photon shot noise limited sensitivities of 10^{-20} W Hz^{-1} (slope) and 10^{-12} W Hz^{-1/2} (variance) are achievable. This work lays the groundwork for further optimisation of NV-based RF detectors.