Spontaneous collapse models provide a possible, testable solution to the quantum measurement problem. While experiments are providing increasingly stronger bounds on their parameters, a full-fledged relativistic extension is still missing. Previous attempts have encountered different obstacles, such as violation of microcausality, infinite energy rate, and particle production from vacuum. Here, we propose a generalization of the collapse master equation that is characterized by a local field collapse operator and a non-Markovian noise with a Lorentz invariant correlation. Our construction is able to overcome previously encountered problems and has the desirable properties in the nonrelativistic limit. A specific choice of the noise correlation function is also introduced and discussed.

Exploring the shareability and distribution of entanglement possesses fundamental significance in quantum information tasks. In this paper we demonstrate that the square of bipartite entanglement measures $G_q$-concurrence, which is the generalization of concurrence, follows a set of hierarchical monogamy relations for any $N$-qubit quantum state. On the basis of these monogamy inequalities, we render two kinds of hierarchical indicators that exhibit evident advantages in the capacity of witnessing entanglement. Moreover, we show an analytical relation between $G_q$-concurrence and concurrence in $2\otimes d$ systems. Furthermore, we rigorously prove that the monogamy property of squared $G_q$-concurrence is superior to that of squared concurrence in $2\otimes d_2\otimes d_3\otimes \cdots \otimes d_N$ systems. In addition, several concrete examples are provided to illustrate that for multilevel systems, the squared $G_q$-concurrence satisfies the monogamy relation, even if the squared concurrence does not. These results better reveal the intriguing characteristic of multilevel entanglement and provide critical insights into the entanglement distribution within multipartite quantum systems.

Continuous-time quantum walks offer provable speedups for certain computational problems, yet translating these advantages to near-term hardware remains challenging. We realize variational ansätze based on continuous-time quantum walks on an analog neutral-atom processor. For unentangled targets, we derive closed-form expressions for near-optimal control parameters that transfer directly to hardware with minimal calibration. On QuEra's Aquila processor, we observe the superquadratic convergence characteristic of efficient quantum walk algorithms, visible at low circuit depth, with theory predicting stronger speedups as hardware improves. For entangled targets, specifically symmetric superpositions in the Rydberg-blockaded subspace, we introduce an optimization protocol exploiting spectral properties of the walk dynamics. The required evolution timescales inversely with the spectral gap, offering an advantage over adiabatic protocols, whose evolution timescales as the inverse square of the spectral gap. We verify this scaling behavior on Aquila and confirm that the prepared states are coherent superpositions via quench dynamics. Our results establish a practical pathway from abstract quantum walk algorithms to analog quantum processors, demonstrating that the dynamics underlying their potential for superquadratic quantum speedup are accessible on current devices.

We investigate open-loop quantum state preparation for a class of open quantum systems whose dynamics follow a Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation that admits a trajectory-based stochastic representation. The deterministic control objective is reformulated as a stochastic optimal control problem—interpreting stochasticity as a methodological tool akin to stochastic Schrödinger equation unravelings—which situates the problem within the path integral control framework. For the class of GKLS generators under consideration, this reformulation leads to an explicit expression for the optimal control as a weighted average over stochastic quantum trajectories, thereby eliminating the need for gradient evaluations. Building on this theoretical result, we derive a control update rule for piecewise-constant control pulses and demonstrate that adaptive importance sampling progressively enhances the control estimator during optimization, culminating in the algorithm we term Path integral Quantum Control (PiQC). We further introduce an annealed variant of PiQC, wherein a synthetic noise schedule gradually steers open-system trajectories toward closed-system dynamics, enabling high-fidelity unitary state preparation. Numerical studies on a dissipative single-qubit system and a multiqubit Nuclear Magnetic Resonance model verify that PiQC yields precise open-loop controls and displays robustness to Hamiltonian perturbations. We propose PiQC as a trajectory-based alternative to gradient-based approaches, which might offer a viable solution in quantum control problems where gradient computation is infeasible or computationally demanding.

Quantum state transformations and resource reversibility in quantum resource theories have always been of interest to researchers. It is well known that quantum catalysts can enhance the capabilities of quantum state transformations. Previous studies have shown that bound magic states are asymptotically irreversible for qudit systems with odd-prime dimensions. This paper focuses on the reversibility in asymptotic manipulations in magic state resource theory with the assistance of catalysis. First, by introducing the definitions of distillable magic, magic cost, and magic of formation, we establish the equivalence relationship between magic cost and regularized magic of formation. Furthermore, we prove that no magic resources can be distilled from bound magic states even if the correlating catalysis is assisted under permissive choices of free operations. This result resolves the question about whether catalysis can reverse the irreversibility of bound magic states within the odd-prime qudit framework, and it rules out the possibility that catalysis can make magic resource theory asymptotically reversible.

With the rapid development of quantum computers in recent years, the importance of performance evaluation in quantum algorithms has been increasing. One method that has gained attention for performing this evaluation on classical computers is tensor networks. Tensor networks not only reduce the computational cost required for simulations by using approximations but are also deeply connected to entanglement. Entanglement is one of the most important elements for the quantum advantages of quantum algorithms, but the direct relationship between quantum advantages and entanglement remains largely unexplored. Tensor networks are promising as a means to address this question. In this study, we focus on the entanglement in the quantum approximate optimization algorithm (QAOA). This study aims to investigate entanglement in QAOA by examining the relationship between the approximation rates of tensor networks and the performance of QAOA. Specifically, we actually perform tensor network simulations of QAOA on a classical computer and extend the study of the scaling relations presented in previous research. We have discovered that scaling relations hold even when entanglement entropy is used as the vertical axis in QAOA solutions of the MAXCUT problem. Furthermore, by analyzing the results of the numerical calculations, we propose a function for the scaling relation. Additionally, we discovered interesting relationships regarding the behavior of entanglement in QAOA during our analysis. This research is expected to provide insights into the theoretical foundation of the scaling relations presented in previous studies.

We report on magneto-optical trapping of the two fermionic isotopes of atomic titanium, ${}^{47}\mathrm{Ti}$ and ${}^{49}\mathrm{Ti}$. Unlike the even mass-number isotopes, which were recently laser cooled, ${}^{47}\mathrm{Ti}$ and ${}^{49}\mathrm{Ti}$ have nonzero nuclear spins and, consequently, their atomic levels are split by hyperfine structure. Combining and comparing theoretical calculations and atomic beam-spectroscopy measurements, we determine the hyperfine structures and isotope shifts of the $3d^{2}4s^2$ $a^3{F}_4\to 3d^2{(}^{3}P)4s4p{(}^3{P}^o)$ $y^5{D}_4^o$ optical-pumping transition at optical wavelength $391\mathrm{nm}$ and the $3d^3{(}^{4}F)4s$ $a^5{F}_5\to 3d^3{(}^{4}F)4p$ $y^5{G}_6^o$ laser-cooling transition at wavelength $498\mathrm{nm}$. With this information, we produce magneto-optical traps of both ${}^{47}\mathrm{Ti}$ and ${}^{49}\mathrm{Ti}$ by applying two additional tones of light to repump atoms to the maximum-spin states on the laser-cooling transition. Directly loading from the atomic flux of a titanium sublimation pump, we produce ${}^{47}\mathrm{Ti}$ and ${}^{49}\mathrm{Ti}$ traps with 731(190) and 1142(240) atoms, and with lifetimes of $330\left(15\right)$ and $310\left(8\right)\mathrm{ms}$, respectively.

The positronium ion $\left({\mathrm{Ps}}^{-}\right)$, a Coulombic three-body bound state of two electrons and a positron, predominantly decays via electron-positron annihilation into electromagnetic final states. While its radiative decay channels have been extensively studied, much less attention has been given to weak processes in this system. In this work, we investigate the rare decay ${\mathrm{Ps}}^{-}\to e^{-}{\nu }_{\mu }{\overline{\nu }}_{\mu }$, obtained by replacing the photon in ${\mathrm{Ps}}^{-}\to e^{-}\gamma$ with a virtual $Z$ boson. Treating the three-body process as an effective two-body transition, ${\mathrm{Ps}}^{-}\to e^{-}{Z}^{*}(\to {\nu }_{\mu }{\overline{\nu }}_{\mu })$, we compute the decay rate by explicitly evaluating all spin configurations of the initial-bound-state and final-state particles. The result agrees with that obtained using the standard spin-summation formalism of quantum field theory. We find that the branching ratio is comparable to that of the weak decay of ortho-positronium, $\mathrm{o}\text{−}\mathrm{Ps}\to \gamma \nu \overline{\nu }$.

The dynamics of relativistic vortex electrons in laser fields is typically studied under the assumption of normal laser incidence, a configuration that preserves the transverse topological structure. In practical experiments, however, perfectly normal incidence is hard to achieve and oblique incidence is often unavoidable. In this work, we extend the Volkov-Bessel formalism to describe a vortex electron interacting with an obliquely incident plane-wave laser field and derive approximate analytical solutions in a small-angle approximation. The analytical results and numerical simulations reveal that oblique incidence induces splitting and rotation of the transverse probability density, arising from anisotropic contributions of the radial and azimuthal currents. Potential applications in the generation, diagnosis, and optical manipulation of relativistic vortex electrons are also discussed.

Odd-even high-order harmonic generation (HHG) from oriented polar molecules encodes intrinsic molecular asymmetry on a subcycle timescale, yet a complete set of amplitude-phase observables connecting spectral measurements to microscopic emission dynamics has remained elusive. In this study, we identify a complete amplitude-phase observable set linking spectral asymmetry, namely, odd-even intensity and phase difference, to amplitude and phase asymmetry of consecutive attosecond bursts through an explicit and invertible mapping. We show that these spectral and microscopic quantities provide equivalent signatures of molecular asymmetry within a subcycle interferometric picture, revealing parity-resolved electron rescattering cross sections associated with the symmetric and antisymmetric components of the molecular wave function. Numerical solutions of the time-dependent Schrödinger equation for oriented CO validate the proposed framework. These results establish odd-even HHG as a unified amplitude-phase probe of molecular asymmetry, enabling quantitative tracking of attosecond asymmetry dynamics directly from spectral measurements.

We study the out-of-equilibrium dynamics of an attractively interacting impurity suddenly immersed with a nonzero initial velocity into a system of one-dimensional weakly interacting homogeneous bosons. We uncover and characterize different dynamical regimes in the parameter space. Especially interesting is the relaxation of a fast impurity with a mass close to or exceeding the critical one, where the impurity exhibits undamped temporal long-lived velocity oscillations before reaching a stationary state. The underlying mechanism is the transient localization of a boson depletion cloud near the impurity that oscillates around the boson density peak situated at the impurity position. The lifetime of this oscillating state increases with the absolute value of the impurity-boson coupling. Cold atomic gases provide an ideal playground where this phenomenon can be probed.

Spatiotemporal vortex pulses (STVPs) are wavepackets that carry transverse orbital angular momentum (OAM) whose proper quantification has been the subject of recent debate. In this work, we introduce a simplified mechanical model of STVPs, consisting of a loop of noninteracting point particles traveling at a uniform constant speed but at slightly different angles. We examine different initial conditions for the particle loop, including configurations that are elliptic in space at a given time and configurations that are elliptic in spacetime at a fixed propagation distance. Furthermore, by employing a nonuniform mass distribution, the particle loop can mimic an STVP not only in configuration space, but also in momentum space. Remarkably, when supplemented by a semiclassical vorticity quantization condition, our mechanical model exactly reproduces different wave-based OAM results previously reported for paraxial STVPs.

We report the dynamics of a single-mode squeezed vacuum in evanescently coupled waveguide arrays incorporating next-nearest-neighbor coupling (NNNC) and disorder. Using an extended tight-binding framework, we show that NNNC reshapes the system's dispersion (phase), breaks spectral symmetry, and introduces alternative quantum pathways for the evolution of quadrature squeezing. This leads to a squeezing revival, squeezing transfer, squeezed quadrature swapping within a mode $(Q\leftrightarrow P)$, and partial confinement of quantum noise near the excitation site in a larger waveguide array. Both on-site disorder (OSD) and hopping disorder (HoD) degrade local squeezing, localizing quantum noise to a few modes, where moderate NNNC enhances this confinement and stronger NNNC counteracts it in larger waveguide lattices. An analytical and numerical analysis of the model suggests that NNNC partially preserves local mode squeezing by providing alternative quantum routes for quadrature rotation, even in the presence of disorder. These results suggest a mechanism for engineering quantum-noise transport in integrated photonic lattices, where disorder and next-nearest coupling make the model more realistic for on-chip quantum technologies.

Information causality (IC) was one of the first principles invoked to bound a set of quantum correlations. For some families of correlations, this principle recovers exactly the boundary of the quantum set; for others, there is still a gap. We close some of these gaps using a quantifier for IC based on the notion of redundant information. This progress was made possible by the recognition that the principle of IC can be captured without referring to the success criterion of random access codes. We give strong numerical evidence that this definition is still obeyed by quantum correlations in the same scenario.

High-fidelity entangling gates in trapped-ion processors are most commonly realized by spectrally isolating a single motional bus mode. As the ion chain grows, however, the coupling of each ion to any one mode weakens, making single-mode gates progressively slower. Existing multimode schemes offer a partial remedy but rely on perturbative driving and rotating-wave approximations, imposing trade-offs between speed and fidelity that become more severe with chain length. We introduce a nonperturbative magnetic-gradient scheme in which all axial motional modes participate collectively in mediating the entangling interaction. Exact spin-motion decoupling is enforced at the end of the protocol by construction, so that the achievable gate speed is limited only by the available gradient strength and control bandwidth. The framework supports both multiqubit gates and selective two-qubit gates between arbitrary pairs in a linear string, including simultaneous operation on multiple pairs, and remains effective as the ion number increases.

Lindbladian quantum master equations (LEs) are the most popular descriptions for quantum systems weakly coupled to baths. But, recent works have established that in many situations, such Markovian descriptions are fundamentally limited: they cannot simultaneously capture populations and coherences even to leading order in system-bath couplings. This can cause a violation of fundamental properties like thermalization and continuity equations associated with local conservation laws, even when such properties are expected in the actual setting. This begs the question: given a physical situation, how do we know if there exists an LE that describes it to a desired accuracy? Here we show that, for both equilibrium and nonequilibrium steady states, this question can be succinctly formulated as a semidefinite program (SDP), a convex optimization technique. If a solution to the SDP can be found to a desired accuracy, then an LE description is possible for the chosen setting. If not, no LE description is fundamentally attainable, showing that a consistent Markovian treatment is impossible even at weak system-bath coupling for that particular setting. Considering a few qubit isotropic XXZ-type models coupled to multiple baths, we find that in most parameter regimes, LE description giving accurate populations and coherences to leading order is unattainable, leading to rigorous no-go results. However, in some cases, the LE description having correct populations but inaccurate coherences, and satisfying local conservation laws, is possible over some of the parameter regimes. Our work highlights the power of semidefinite programming in the analysis of physically consistent LEs in understanding the limits of Markovian descriptions at weak system-bath couplings.

We evaluate the role of quantum coherence as a thermodynamic resource in a noisy, Markovian, one-qubit heat engine. By consuming the coherence of noisy quantum states, we demonstrate that the engine can surpass the classical efficiency limit when operating according to a quantum Otto cycle. The engine's nonclassical nature is demonstrated by its violation of the Leggett-Garg temporal correlations inequality. Amplitude damping increases the extractable work under partial thermalization, thereby increasing the efficiency. In contrast, phase damping increases the extractable work under partial thermalization but reduces the efficiency. We implement the entire Otto cycle in a quantum circuit, simulating realistic amplitude and phase damping channels, as well as gate-level noise. We introduce an operational measure of the circuit's thermodynamic cost to establish a direct link between energy consumption and information processing in quantum heat engines.

In multiparameter quantum estimation, the optimal measurements for different parameters encoded in a quantum state are in general incompatible, giving rise to nontrivial tradeoffs between their attainable levels of precision. Understanding and characterizing such tradeoffs is essential for determining the ultimate precision limits in multiparameter quantum estimation, and it is therefore a central topic in quantum metrology. In this article, we present an approach that precisely quantifies the tradeoff resulting from incompatible optimal measurements in multiparameter estimation. We derive a tight analytical tradeoff relation that determines the ultimate precision limits for estimating an arbitrary number of parameters encoded in pure quantum states. Additionally, we provide a systematic methodology for constructing optimal measurements that saturate this tight bound in an analytical and structured manner. To demonstrate the power of our findings, we apply our methodology to quantum radar, resulting in a refined Arthurs-Kelly relation that characterizes the ultimate performance for the simultaneous estimation of range and velocity.