While the information processing of organisms is evolutionarily optimized, it exhibits remarkable diversity in its complexity and capability. One potential source of this diversity is the limitations of resources available for information processing. However, we still lack a theoretical framework that clarifies the relationship between biological information processing and resource limitations and integrates it with downstream decision-making. Together with the accompanying letter [Tottori and Kobayashi, Phys. Rev. Res. 7, L042012 (2025)], this full paper presents an optimal estimation and control framework that explicitly incorporates resource limitations inherent in biological systems. While the accompanying letter focuses on the nontrivial phase transitions induced by resource limitations, the present full paper establishes the theoretical foundation and provides a comprehensive analysis of these transitions. The proposed framework formulates memory that organisms can store and operate, and optimizes it using optimal control theory. This approach accounts for various resource limitations—such as memory capacity, intrinsic noise, and energy cost—and unifies estimation and control. Applying this theory to minimal models of biological information processing and decision-making, we demonstrate that resource limitations can induce discontinuous and nonmonotonic phase transitions between memoryless and memory-based strategies. These results provide a comprehensive theoretical foundation for studying how organisms process information and make decisions under resource limitations, and suggest that the rich diversity observed in biological systems may emerge from such constraints.

The low coercive field ($E_c$) is highly desirable for developing efficient and durable ferroelectric-based devices. However, fluorite ferroelectrics such as ${\mathrm{HfO}}_2$ and ${\mathrm{ZrO}}_2$, which are attracting significant attention as next-generation semiconductor materials due to their compatibility with complementary metal-oxide-semiconductor technology and robust ferroelectric properties, exhibit a significantly high $E_c$, severely limiting their application in memory devices. Here, using group theory and first-principles simulations, we reveal that phonon engineering can induce a new soft mode in the polar $Pca{2}_1$ phase of ${\mathrm{HfO}}_2$ and ${\mathrm{ZrO}}_2$. This mode dominates the intermediate transition state during polarization switching and drastically reduces the energy barriers for both homogeneous switching and the uniquely observed local switching, which enables ultrahigh memory density. Furthermore, the discovery of a ternary state during local switching points to the possibility of implementing ternary logic at the material level. Our findings introduce a new pathway to lowering $E_c$ in fluorite ferroelectrics by exploiting intrinsic lattice dynamics, offering an alternative to conventional strategies such as doping or defect engineering, and open a promising direction for future material design.

Chirality is a fundamental symmetry concept relevant to many scientific fields. It describes discrete states, i.e., left-handed, right-handed, or achiral. In contrast to this discrete classification, objects can be continuously distorted. To describe the deviation from an achiral state, the chirality amplitude has to be addressed, similarly to magnetization being the “amplitude” for time-reversal symmetry breaking. Even though symmetry breaking is the base for many phenomena in science in general, symmetry cannot quantitatively predict measurable quantities. Chirality amplitude is the key quantity for quantifying chirality-related emergent phenomena. Here, we propose two types of chiral lattice distortions and report their ultrafast dynamics. We determine the ultrafast reduction of the chirality amplitude in ${\mathrm{CsCuCl}}_3$ after an optical excitation by using resonant x-ray diffraction with circular polarization. An additional symmetry breaking representing a nonhanded chiral structure is observed by resonant x-ray diffraction when exciting the material with an intense, low-cycle terahertz pulse. The latter demonstrates a hidden enantiomorphic pair in a nonhanded chiral structure. The concept of chirality amplitude, as well as the decomposition into two different types of chiral lattice distortions, suggests a unique approach toward controlling chirality-induced emergent phenomena.

Vector magnetometers based on the optically detected magnetic resonance (ODMR) of nitrogen-vacancy centers in diamond are being developed for applications such as navigation and geomagnetism. However, at low magnetic fields, such as that on Earth ($\sim 50\mu \mathrm{T}$), diamond magnetometers suffer from spectral congestion whereby ODMR peaks are not easily resolved. Here, we experimentally investigate a potential solution of using an isotropic, three-dimensional magnetic flux concentrator to amplify Earth’s field without altering its direction. The concentrator consists of six ferrite cones, in a face-centered cubic arrangement, centered about a diamond. We vary the direction of a $50\mu \mathrm{T}$ applied field and record and fit the resulting ODMR spectra. By comparing the fitted fields to those of a reference fluxgate magnetometer, we characterize the angular response of the diamond magnetometer and quantify absolute errors in the field magnitude and angle. We find that the enhancement factor is nearly isotropic, with a mean of 19.05 and a standard deviation of 0.16, when weighted by solid angle coverage. Gradient broadening of the ODMR lines is sufficiently small that the spectra are well resolved for nearly all field directions, alleviating spectral congestion. For $\sim 98\%$ of the total $4\pi$ solid angle, Cramér-Rao lower bounds for magnetic field estimation uncertainty are within a factor of 2 of those of the fully resolved case, indicating minimal deadzones. We track the stability of the magnetometer over 6 h and observe variations $\lesssim 40\mathrm{nT}/\mathrm{h}$, limited by temperature drift. Our study presents a route for diamond vector magnetometry at Earth’s field, with potential applications in geomagnetic surveys, anomaly detection, and navigation.

Quantum-selected configuration interaction (QSCI) utilizes an input quantum state on a quantum device to select important bases (electron configurations in quantum chemistry) that define a subspace in which to diagonalize a target Hamiltonian, i.e., perform selected configuration interaction, on classical computers. Previous proposals for preparing a good input state, which is crucial for the quality of QSCI, based on optimization of quantum circuits may suffer from optimization difficulty and require many runs of the quantum device. Here, we propose using a time-evolved state by the target Hamiltonian (for some initial state) as an input of QSCI. Our proposal is based on the intuition that the time evolution by the Hamiltonian creates electron excitations of various orders when applied to the initial state. We numerically investigate the accuracy of the energy obtained by the proposed method for quantum chemistry Hamiltonians describing electronic states of small molecules. Numerical results reveal that our method can yield sufficiently accurate ground-state energies for the investigated molecules. Systematic analysis when increasing the number of qubits in a hydrogen chain shows that the subspace size required for sufficiently accurate results is reasonable at system sizes that cannot be solved by naive classical diagonalization. Our proposal provides a systematic and optimization-free method to prepare the input state of QSCI and could contribute to practical applications of quantum computers in quantum chemistry calculations.

Foraging is a complex spatiotemporal process that is often described with stochastic models. Two particular ones, Lévy walks and intermittent search, became popular in this context. Researchers from the two communities, each advocating for either Lévy or intermittent approach, independently analyzed foraging patterns and reported agreement between empirical data and the model they used. We resolve this Lévy-intermittent dichotomy for eye-gaze trajectories collected in a series of experiments designed to stimulate free foraging for visual information. By combining analytical results, statistical quantifiers, and basic machine learning techniques, we devise a method to score the performance of the models when they are used to approximate an individual gaze trajectory. Our analysis indicates that the intermittent search model consistently yields higher scores and thus approximates the majority of the eye-gaze trajectories better.

Significant work has been done to develop quantum satellites, which generate entangled pairs in space and distribute them to ground stations separated some distance away. The reverse “uplink” case, where pairs are generated on the ground and swapped on the satellite using an optical Bell measurement, has not been seriously considered due to a prevailing assumption that it is practically infeasible. In this paper, we illustrate the feasibility of performing Discrete Variable photonic Bell measurements in space by conducting a detailed numerical analysis to estimate the channel efficiency and attainable pair fidelity for various satellite-station configurations. Our model accounts for a wide range of physical effects such as atmospheric effects, stray photons, and mode mismatch. Our findings show promise toward the feasibility of photonic Bell measurements in space, which motivates future research toward large-scale satellite-based uplink entanglement distribution.

We report dispersive spin shot noise measurement of a Bose-Einstein condensate (BEC). While dispersive probing has been used for quantum spin noise measurement of thermal and cold gases for decades, confirmative measurement of shot noise of real spin, i.e., the linear dependence of the spin variance on the number of atoms in a BEC, has been lacking. Here, we demonstrate precise spin noise measurement of a BEC of rubidium atoms at the spin shot noise level by polarization rotation using a two-color probe at optimal detunings, with power balance stabilization to suppress probe-induced excess spin noise. This work opens the possibility for the unexplored study of quantum spin fluctuations in multicomponent or spinor BECs and offers an approach to improve spin measurement precision, which is relevant to atomic spin-based sensors.

Two-photon interference is a cornerstone of quantum optics, enabling imaging, sensing, and precision measurements that surpass classical limits. By harnessing the quantum interference of photon pairs, as demonstrated by the Hong-Ou-Mandel effect, this approach offers superior axial resolution and intrinsic dispersion cancellation, along with strong noise suppression arising from the precise temporal correlations between photons. Building on these principles, we present the theoretical framework and experimental realization of phase-dependent quantum optical coherence tomography (QOCT), a technique that employs phase-modulated two-photon interference for noninvasive morphological analysis of multilayered samples. We demonstrate that introducing controlled phase shifts to photon pairs in a Hong-Ou-Mandel interferometer effectively eliminates artifacts caused by reflections at different sample layers, thereby greatly improving the accuracy and reliability of QOCT measurements. This work advances the fundamental understanding and practical deployment of two-photon interference, overcoming a key limitation in applying QOCT to real-world applications such as biomedical imaging and materials characterization.

Phases manifesting topological patterns in functional systems, like ferroelectric and ferromagnetic vortex superlattices, can manifest intricate and apparently ungovernable behavior, typical of frustrated nonergodic states with high-dimensional energy landscapes. This is also the case for potassium-tantalate-niobate (KTN) crystals. These transparent ferroelectrics manifest remarkable but little understood metastable domain patterns at optical (micrometer and above) scales near the cubic-to-tetragonal structural phase transition. Here, we formulate the topological breakdown model based on the competition between intrinsic scales of domain-domain collinear and noncollinear interactions associated with polarization-charge screening. The model is able to explain observed KTN mesoscopic domain patterns and phase diagram as a function of temperature and external electric field. Findings include a precise set of sharp and broad percolative transitions that are experimentally verified, validating our model. Our study identifies the central role played by competing topologically protected states, identifying a fundamental link between topological protection and frustration that supports a hitherto unexplored functional nonergodic arena.

We emulate the Tolman-Oppenheimer-Volkoff (TOV) equations, including tidal deformability, for neutron stars using a method based upon the Dynamic Mode Decomposition. This method, which we call Star Log-extended eMulation (SLM), utilizes the underlying logarithmic behavior of the differential equations to enable accurate emulation of the nonlinear system. We show predictions for well-known equations of state (EOSs) with fixed parameters using the SLM, accurately recreating high-fidelity results while achieving a computational speedup of $\approx 2.4\times {10}^4$. We test our parametric SLM method for a two-parameter quarkyonic EOS against high-fidelity RK4 TOV calculations and find a computational speedup of $\approx 7.0\times {10}^4$. Hence, SLM is an efficient emulator for the numerous TOV evaluations required by multimessenger astrophysical frameworks that infer constraints on the EOS. The ability of the SLM algorithm to learn a mapping between parameters of the EOS and subsequent neutron star properties also opens up potential extensions for assisting in computationally prohibitive uncertainty quantification for any type of EOS. The source code for the methods employed in this work is openly available in a public GitHub repository for community modification and use.

Quantum spintronics is an emerging field focused on developing novel applications by utilizing the quantum coherence of magnetic systems. A key challenge in this context is achieving scalable long-range quantum information transmission in magnetic systems. Here, we propose a novel transmission scheme based on topological spin textures in a hybrid architecture combining a magnetic racetrack and localized spin qubits. We demonstrate this principle by employing the domain wall (DW)—the most fundamental texture—to transport quantum signal between distant qubits. We introduce a measurement-free protocol that utilizes DW mobility to enable high-fidelity and tunable entanglement generation. Furthermore, we demonstrate that spin qubits can function as quantum stations on the racetrack, enabling flexible state transfer among fast-moving DWs on a single track. Finally, we discuss concrete material platforms to implement the proposed scheme. Our work introduces a new hybrid quantum platform that merges topological spin textures with solid-state qubits, offering a scalable architecture for quantum information processing and opening promising directions for quantum spintronics.

We study the distribution of overlaps with the computational basis of a quantum state generated under generic quantum many-body chaotic dynamics, without conserved quantities, for a finite time $t$. We argue that, scaling time logarithmically with the system size $t\propto logL$, the overlap distribution converges to a universal form in the thermodynamic limit, forming a one-parameter family that generalizes the celebrated Porter-Thomas distribution. The form of the overlap distribution only depends on the spatial dimensionality and, remarkably, on the boundary conditions. This picture is justified in general by a mapping to Ginibre ensemble of random matrices and corroborated by the exact solution of a random quantum circuit. Our results derive from an analysis of arbitrary overlap moments, enabling the reconstruction of the distribution. Our predictions also apply to Floquet circuits, i.e., in the presence of mild quenched disorder. Finally, numerical simulations of two distinct random circuits show excellent agreement, thereby demonstrating universality.

The translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle’s orientation and its rotational Brownian motion. In the overdamped limit, the stochastic evolution of the orientation vector follows a diffusion process on the unit sphere and is characterized by an orientation-dependent (“multiplicative”) noise. As a consequence, the corresponding Langevin equation attains different forms depending on whether Itō’s or Stratonovich’s stochastic calculus is used. We clarify that both forms are equivalent and derive them in a top-down approach from a geometric construction of Brownian motion on the unit sphere, based on infinitesimal random rotations. Our approach suggests further a geometric integration scheme for rotational Brownian motion, which preserves the normalization constraint of the orientation vector exactly. We show that a simple implementation of the scheme, using Gaussian random rotations, converges weakly at order 1 of the integration time step, and we outline an advanced variant of the scheme that is weakly exact for an arbitrarily large time step. Due to a favorable prefactor of the discretization error, already the Gaussian scheme allows for integration time steps that are one order of magnitude larger compared to a commonly used algorithm for rotational Brownian dynamics simulations based on projection on the constraining manifold. For torques originating from constant external fields, we prove by virtue of the Fokker-Planck equation that the constructed diffusion process satisfies detailed balance and converges to the correct equilibrium distribution. The analysis is restricted to time-homogeneous rotational Brownian motion (i.e., a single rotational diffusion constant), which is relevant for axisymmetric particles and also chemically anisotropic spheres, such as self-propelled Janus particles.

The realization and control of collective quantum effects so far have predominantly focused on cold atomic ensembles. Quantum photonic platforms, with their engineered Green's functions and integration capability of advanced solid-state quantum emitters, provide opportunities to explore regimes of light-matter interaction beyond the scope of atomic systems. In this work, we demonstrate that embedding quantum emitters within a thin dielectric layer fundamentally alters their collective radiative behavior. The optical modes in the dielectric layer mediate long-range dipole-dipole interactions between emitters, enabling both total and directional superradiance between emitters separated by several wavelengths. Crucially, this mechanism supports Dicke superradiance even in parameter regimes where standard settings fail to support an interaction, unveiling a dimensionality-driven enhancement of cooperative effects. By bridging many-body quantum optics and photonic engineering, our work reveals a distinct interplay between surrounding dimensionality and collective quantum dynamics. Experimental realization of these predictions, readily achievable in solid-state quantum optics platforms, paves the way for scalable, directional quantum light sources and frontiers in many-body quantum optics.

We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducible vertices, each connecting two fermionic lines. The comparison to the exact solution shows that this approximation is only good for rather weak interactions and even then only qualitatively—at least for the nonlinear response function analyzed.

The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies nonperturbatively across a wide range of interactions and temperatures. It gives access to a local, nonperturbative four-point vertex in imaginary and real frequencies, which can be used as input for subsequent computations such as diagrammatic extensions of dynamical mean-field theory. However, computing and manipulating the real-frequency four-point vertex on large, dense grids quickly becomes numerically challenging when the density and/or the extent of the frequency grid is increased. In this paper, we compute four-point vertices in a strongly compressed quantics tensor train format using quantics tensor cross interpolation, starting from discrete partial spectral functions obtained from mpNRG. This enables evaluations of the vertex on frequency grids with resolutions far beyond the reach of previous implementations. We benchmark this approach on the four-point vertex of the single-impurity Anderson model across a wide range of physical parameters, both in its full form and in its asymptotic decomposition. For imaginary frequencies, the full vertex can be represented to an accuracy on the order of $2\times {10}^{-3}$ with maximum bond dimensions not exceeding 120. The more complex full real-frequency vertex requires maximum bond dimensions not exceeding 170 for an accuracy of $\lesssim 2\%$. Our work marks another step toward tensor-train-based diagrammatic calculations for correlated electronic lattice models starting from a local, nonperturbative mpNRG vertex.