A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum limits. Here, we present an approach that precisely quantifies these trade-offs for an arbitrary number of parameters encoded in pure quantum states. Our approach not only derives tight analytical bounds for the trade-offs induced by measurement incompatibility but also provides a systematic methodology to design optimal measurement strategies that saturate these limits. To demonstrate the practical significance of our findings, we apply our framework to quantum radar and obtain a refined Arthurs-Kelly relation that characterizes the ultimate performance for the simultaneous estimation of range and velocity with any given amount of entanglement. This showcases the transformative potential of our findings for a wide range of applications in quantum metrology, sensing, and beyond.

We propose a quantum-error-correction-inspired noise mitigation protocol for enhancing the sensitivity of wavelike dark matter searches with quantum sensors. Our protocol uses multiple sensors to mitigate the noise affecting each sensor individually, allowing for the suppression of excitation noise that is parallel to the dark matter signal. We demonstrate that our protocol can improve the sensitivity to dark matter signals by a factor of $\sqrt{N}$, where $N$ is the number of sensors used, for small $N$. Furthermore, for sufficiently large $N$, we find that our protocol achieves the same performance as the standard quantum limit by the ideal measurement, which nonentangled sensors with parallel noise cannot reach due to the unknown phase of the dark matter field. Our Letter can be widely applied to various types of signals with unknown phases and has the potential to enhance the sensitivity of quantum sensors such as arrays of resonant cavities.

We reexamine the large $N$ limit of $\mathrm{SU}(N)$ symmetric quantum mechanics of a Hermitian matrix whose singlet sector is well known to be exactly solvable via free fermions. When the Fermi level approaches a maximum of the potential, there is critical behavior corresponding to string theory in two dimensions. We uncover new phenomena in the adjoint sector by solving the Marchesini-Onofri equation both numerically and analytically using semiclassical approximations: at criticality, the spectrum is governed by Regge trajectories with energy eigenvalues growing according to ${\mathrm{\Delta }}^2\sim n/{\alpha }^{\prime }$. In the dual 2D string theory, we interpret these states as oscillatory excitations of a “short” folded open string. Up to subleading corrections, this Regge behavior is essentially universal and is insensitive to the particular potential we choose to approach criticality. Slightly away from criticality, the highly excited states transition into “long strings” that extend far into the Liouville direction.

The first observation of the doubly charmed baryon ${\mathrm{\Xi }}_{cc}^{+}$ is reported through its decay to the ${\mathrm{\Lambda }}_c^{+}{K}^{-}{\pi }^{+}$ final state, with a statistical significance exceeding seven standard deviations. The observation is made using proton-proton collision data collected in 2024 with the LHCb Run 3 detector at a center-of-mass energy of 13.6 TeV, corresponding to a total integrated luminosity of $6.9{\mathrm{fb}}^{-1}$. The ${\mathrm{\Xi }}_{cc}^{+}$ mass is measured to be $3619.97\pm 0.83\pm {0.26}_{-1.30}^{+1.90}\mathrm{MeV}/c^2$, where the first uncertainty is statistical, the second is systematic, and the third is due to the unknown ${\mathrm{\Xi }}_{cc}^{+}$ lifetime, which is assumed to lie in the range 15–160 fs with a baseline value of 45 fs. The difference between the masses of the ${\mathrm{\Xi }}_{cc}^{+}$ and ${\mathrm{\Xi }}_{cc}^{++}$ baryons is determined to be $-1.77\pm 0.84\pm {0.15}_{-1.30}^{+1.90}\mathrm{MeV}/c^2$. This is the first observation of a new particle made with the LHCb Run 3 detector.

Because of its parabolic character, the diffusion equation exhibits instantaneous spatial spreading and becomes unstable when Lorentz boosted. According to the conventional interpretation, these features reflect a fundamental incompatibility with special relativity. In this Letter, we show that this interpretation is incorrect by demonstrating that any smooth and sufficiently localized solution of the diffusion equation is the particle density of an exact solution of the relativistic Vlasov-Fokker-Planck equation. This establishes the existence of a causal, stable, and thermodynamically consistent relativistic kinetic theory whose hydrodynamic sector is governed exactly by diffusion at all wavelengths. We further demonstrate that the standard arguments for instability arise from considering solutions that admit no counterpart in kinetic theory and that apparent violations of causality disappear once signals are defined in terms of the underlying microscopic data.

Ramsey resonance is a high-resolution technique used in spectroscopy, precise measurement of time and frequency, and the creation of modern clocks. The Ramsey experiments are typically done in optically dilute samples of atoms to improve homogeneity and avoid backaction of atoms on excitation pulses. In contrast to latter belief, we predict and experimentally show that in optically thick resonant media, the backaction can lead to the highly enhanced narrowing of Ramsey resonance. The linewidth narrowing and corresponding precision of the frequency measurement scale exponentially with an increase in optical depth of a sample and can reach the limits set by homogeneous broadening. We show that this effect is caused by a nonlinear interference of multiple echoes formed inside the atomic medium, which is experimentally confirmed with ${{}^{167}\mathrm{Er}}^{3+}$ ions in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. Our findings open new opportunities for sensitivity enhancement of the Ramsey technique, as well as providing researchers with an additional method to investigate fundamental issues of coherent nonlinear interaction of light pulses with resonant atomic ensembles and numerous applications.

The fluctuation-dissipation theorem connects equilibrium noise to linear response and forms a cornerstone of statistical and quantum physics, yet its extension to geometry-driven nonlinear transport remains largely unexplored. Here we establish a geometric fluctuation-dissipation relation linking dc current noise at linear order to second-order nonlinear responses—specifically shift and injection photocurrents—in the bulk photovoltaic effect of noncentrosymmetric gapped quantum materials. Using a microscopic density-matrix formalism, we show that linear dc current noise in the dc electric field arising from off-diagonal current correlations is universally governed by frequency-integrated nonlinear optical responses and is encoded in the quantum geometry of Bloch states. We further demonstrate that intrinsic and extrinsic noise contributions exhibit distinct symmetry properties and relaxation-time dependencies, corresponding respectively to shift and injection photocurrents. We derive analytical expressions in a generic two-band model and numerically verify them in the Haldane model. Our results establish dc current noise at linear order as a direct probe of quantum geometry and nonlinear optical response in gapped quantum materials, extending fluctuation-dissipation relations well beyond linear equilibrium transport.

Despite major experimental progresses in time-resolved and angle-resolved photoemission spectroscopy, a quantitative, microscopic framework for interpreting exciton-induced modifications of electronic band structures—applicable even beyond the low-density limit—is still lacking. Here, we close this gap by introducing a unified approach that links the dynamics of coherent and incoherent excitons to distinct and experimentally observable excitonic sidebands. Our central result is a general, first-principles formula for time-resolved photoemission spectra, applicable across a broad range of temperatures, excitation densities, and pump-probe delays. This advance provides a predictive tool for quantitatively tracking excitonic dynamics in complex materials.

Flat bands in photonic systems enable strong light confinement and enhanced light-matter interactions, yet realizing flat dispersion across an entire Brillouin zone (BZ) remains nontrivial. Here, we propose a practical mechanism for generating BZ-spanning flat bands through the coupling between $M$ propagating modes and $N$ localized resonances. When $N>M$, the finite-channel model necessarily supports exact flat bands that originate from an effectively decoupled subspace. As a representative example, we implement this mechanism in a plasmonic superlattice, where multiple localized resonances hybridize with surface plasmon polaritons. Angle-resolved reflection measurements directly reveal a quasi-flat band extending across the BZ, in excellent agreement with full-wave simulations. The suppressed group velocity further enlarges the momentum-space separation of quasi-bound-state-in-the-continuum-induced exceptional-point pairs, enabling their experimental observation in a plasmonic platform. Our results establish a practical design strategy for engineering flat bands and non-Hermitian degeneracies, which can be extended to dielectric and hybrid systems across a wide spectral range under appropriate conditions, opening new opportunities for compact photonic devices with enhanced functionality.

Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum mechanics provides an accessible alternative by associating quantum states with classical probability distribution functions called tomograms. Despite its advantages, including compatibility with classical statistical methods, the tomographic method remains underutilized due to a lack of robust estimation techniques. This Letter addresses this gap by introducing a nonparametric kernel quantum state estimation (KQSE) framework for reconstructing quantum states and their trace characteristics from noisy data, without prior knowledge of the state. In contrast to existing methods, KQSE yields estimates of the density matrix in various bases, as well as trace quantities such as purity, higher moments, overlap, and trace distance, with a near-optimal convergence rate of $\tilde{O}(T^{-1})$, where $T$ is the total number of measurements. KQSE is robust for multimodal, non-Gaussian states, making it particularly well suited for characterizing states essential for quantum science.

The Kibble-Zurek mechanism (KZM) predicts the spontaneous formation of topological defects in a continuous phase transition driven at a finite rate. We propose the generation of spontaneous quantum turbulence (SQT) via the KZM during Bose-Einstein condensation induced by a thermal quench. Using numerical simulations of the stochastic projected Gross-Pitaevskii equation in two spatial dimensions, we describe the formation of a newborn Bose-Einstein condensate proliferated by quantum vortices. We establish the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy.

We analyze the effects of various forms of noise on one-dimensional systems of noninteracting fermions. In the strong noise limit, we demonstrate, under mild assumptions, that the statistics of the fermionic correlation matrix in the thermodynamic limit follow a universal form described by the recently introduced quantum simple symmetric exclusion process (QSSEP). For charge transport, we show that QSSEP, along with all models in its universality class, shares the same large deviation function for the transferred charge as the classical SSEP model. The method we introduce to derive this result relies on a gaugelike invariance associated with the choice of the bond where the current is measured. This approach enables the explicit calculation of the cumulant-generating function for both QSSEP and SSEP and establishes an exact correspondence between them. These analytical findings are validated by extensive numerical simulations. Our results establish that a wide range of noisy free-fermionic models share the same QSSEP universality class and show that their transport properties are essentially classical.

Studies of entanglement dynamics in quantum many-body systems have focused largely on initial product states. Here, we investigate the far richer dynamics from initial entangled states, uncovering universal patterns across diverse systems ranging from many-body localization (MBL) to random quantum circuits. Our central finding is that the growth of entanglement entropy can exhibit a counterintuitive nonmonotonic dependence on the initial entanglement in many nonergodic systems, peaking for moderately entangled initial states. To understand this phenomenon, we introduce a conceptual framework that decomposes entanglement growth into two mechanisms: “build” and “move.” The “build” mechanism creates new entanglement, while the “move” mechanism redistributes preexisting entanglement throughout the system. Specifically, we demonstrate that MBL dynamics are “move-dominated,” exhibiting a quantitative agreement with a random SWAP circuit that serves as a model of pure “move” dynamics by uniformly distributing preexisting entanglement. This implies that MBL acts as a redistributor of a hidden entanglement reservoir quantified by the bipartition-averaged entropy. This “build-move” framework offers a unified perspective for classifying diverse physical dynamics, deepening our understanding of entanglement propagation and information processing in quantum many-body systems.

We construct parametrized isometric tensor network states—referred to as “skeletons”—that allow us to explore phases of Abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite correlation length deformations of string-net fixed points, which are constructed both by conserving virtual symmetries of the tensor and by imposing local isometry constraints. They connect distinct topological phases via a shared critical point, thereby providing analytically tractable examples of phase transitions beyond anyon condensation. By mapping such classes of 2D tensor networks to 1D stochastic automata with local update rules, we show that expectation values of generalized Pauli strings of arbitrary weight can be efficiently computed using classical methods. Therefore these skeletons not only serve as an organizing principle for Abelian topological order but also provide a nontrivial test bed for quantum processors.

Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin systems, we study the high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians, which include the special case of geometrically local fermionic systems. We prove that, at a sufficiently high temperature that is independent of the system size, the Gibbs state is a probabilistic mixture of fermionic Gaussian states. This forms the basis of an efficient classical algorithm to prepare the Gibbs state by sampling from a distribution of fermionic Gaussian states.

Quantum resources can, in principle, enable Heisenberg-limited sensing, yet no-go theorems imply that Heisenberg-limited scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use in quantum sensing is constrained by stringent requirements, including prior noise characterization, restrictive signal-noise compatibility conditions, and measurement-based syndrome extraction with global control. Here we introduce a QEC protocol based on indefinite causal order (ICO), providing the first application of ICO to QEC. By coherently placing auxiliary controls and noisy evolution in an indefinite causal order, the resulting noncommutative interference enables an auxiliary system to herald and correct errors in real time, avoiding the entanglement encoding and entanglement readout required by traditional QEC. Furthermore, within the time-reversal regime of the Hamiltonian, our protocol extends correctability to parallel noises where traditional protocols may fail. We rigorously establish the protocol for single-noise and multinoise scenarios and demonstrate its performance in single-qubit, many-body, and continuous-variable platforms. We further identify regimes in which error correction can be implemented entirely by unitary control, without measurements. Our results reveal ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing.