This study explores robust negative quantum states described using the framework of discrete Wigner functions. Notably, these states are known to outperform the Bell state in measures of entanglement in the presence of non-Markovian noise. Our study focuses on developing and implementing quantum circuits for generating these states on superconducting hardware, and realizing them on IBM's ibm_brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages these entangled states as a resource. Furthermore, these states are found to perform better than the Bell states for maximal Clauser-Horne-Shimony-Holt  violation and maximal mean quantum Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent.

Bosonic systems, particularly in quantum optics and atomic physics, are leading platforms for achieving quantum-enhanced precision in parameter estimation. By exploiting properties such as mode and particle entanglement, it is possible to attain precisions that surpass the shot-noise limit with respect to key resources like probe number or energy. Yet the mechanisms by which these bosonic resources enable quantum enhancement remain unclear. Consequently, the design of optimal probes and evolutions often relies on case-by-case analyses, where continuous- and discrete-variable regimes are treated separately and their connection is still unclear. We develop a comprehensive framework for quantum metrology that unifies all known precision-enhancement mechanisms based on bosonic systems. Our approach employs a superselection-rule–compliant representation of the electromagnetic field that explicitly includes the phase reference, thereby enforcing total particle-number conservation and bridging the discrete and continuous limits of quantum optics and symmetric massive systems. Within this unified formalism, of which established results emerge as special cases, we identify the distinct roles of mode and particle entanglement for quantum-enhanced precision. The framework further provides general measurement-optimization strategies for arbitrary multimode entangled probe states and naturally incorporates noise and nonunitary dynamics, ensuring applicability to realistic experimental conditions.

High-dimensional entanglement (HDE) is a valuable resource in quantum information processing, and efficient certification of HDE is crucial to many applications. In this work, we propose a simple and general framework for certifying HDE in general bipartite pure states under restricted operations, such as local operations and classical communication (LOCC). On this basis, we show that HDE in general bipartite pure states can be certified efficiently. Moreover, the sample cost required to certify a given degree of HDE even decreases monotonically with the local dimensions. In addition, for a general two-qubit pure state, we construct an optimal entanglement certification strategy based on separable operations, which can be realized by LOCC when the target state has sufficiently high entanglement. The core concept of our framework is versatile and can be extended to certify a wide range of critical quantum resources under restricted operations.

Global-scale entanglement distribution has been a formidable challenge due to the unavoidable losses in communication channels. Here we propose a backbone channel for a quantum network based on balloon-based aerial relays. We demonstrate that the atmospheric disturbances in balloon-based channels can be almost eliminated through optimizing beam waist positions and employing a series of adaptive optics systems, which boosts the channel efficiency to –21 dB over a 10 000 km distance, outperforming satellite-based relays by 12 dB with the same device parameters. We then propose a global-scale quantum networking scheme based on hybrid-channel quantum repeaters that combine ground-based quantum repeaters and balloon-based aerial relays. Servers are interconnected globally via a chain of balloons, while multiple clients link to local servers through fiber connections, facilitating rapid client switching and network scalability. Our simulations, employing state-of-the-art ${\mathrm{Eu}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ quantum memories and mature entanglement sources based on spontaneous parametric down-conversion, demonstrate an entanglement distribution rate in the subhertz range between clients separated by 10 000 km. This approach offers a practical path toward global quantum networking in the near future.

Rotations play a detrimental role in achieving ultra-high-performance inertial measurements with an atom interferometer, leading potentially to a total loss of interference contrast and the emergence of dominant phase-shift biases. This becomes particularly significant when considering operation in dynamic conditions such as those encountered by Earth-orbiting satellites in the perspective of future space gravity missions onboarding a cold-atom accelerometer. In this context, we perform an experimental study of the impact of rotation on an atom interferometer and investigate mitigation strategies. Using an original setup in which the well-controlled proof mass of a space electrostatic accelerometer is used as the retroreflection mirror of a cold-atom gravimeter, we are able to measure both the contrast and phase shift of the interferometer especially for low and high angular accelerations. Thanks to an analytical model, we are able to explain the origin of the measured contrast loss and phase shifts arising from the different inertial accelerations. By properly counterrotating the electrostatic proof mass, we demonstrated a contrast, otherwise equal to zero, to a level better than 90%, for both constant angular velocities and for important angular accelerations. For constant angular velocities, our model retrieves the experimental data with an error of $25\mathrm{m}\mathrm{rad}$, in agreement with the experimental uncertainty. Our results demonstrate the possibility to perform high-performance inertial measurements with a cold-atom interferometer in challenging environments by demonstrating a high contrast recovery and the precise determination of the rotation-induced phase-shift bias.

We explore the Mott insulating phases of dual-species bosonic spinor lattice gases, emphasizing the intriguing interplay between synthetic flux and interspecies spin exchange interaction. One of the species is subjected to Raman-assisted tunneling, which leads to a synthetic flux within the framework of synthetic dimensions. In the deep Mott regime, the low-energy physics is governed by an unconventional and highly tunable spin model, which is characterized by two distinct spin chains. The synthetic flux serves as an effective spin-orbit coupling, inducing Dzyaloshinskii-Moriya (DM) interactions in one of the spin chains. The interspecies spin exchange interaction gives rise to the inter-chain coupling embodied as an isotropic $\mathit{XX}$ interaction. Using time-evolving block decimation method for tensor network states, we compute order parameters, correlation functions and structure factors to identify the ground state magnetic phases. The DM interaction in one species, when combined with the interspecies spin-exchange interaction, can induce spiral magnetic order in the second, otherwise nonchiral species. Additionally, the interplay of a transverse field applied to one spin chain and the interspecies coupling can drive both spin chains into a paramagnetic phase simultaneously. These results reveal that interspecies coupling serves as a powerful conduit for transmitting magnetic correlations, enabling exotic phases beyond the single-component perspective.

Virtual critical coupling (VCC) optimizes coupling from a bus waveguide into a resonator by shaping the optical input into a truncated, increasing exponential pulse to excite the resonator's complex transmission zero. This approach is challenging at optical frequencies due to broadband modulation requirements and strong sensitivity to dispersion. Moreover, its adaptation to resonators with non-negligible intrinsic loss remains unclear. In this work we develop a general theory of VCC for chains of generally lossy coupled resonators to address these issues. First, we prove analytically that as the number of resonators increases, VCC can be achieved with smoother inputs and delayed outputs, improving ease of generation and robustness to dispersion. Second, we show that when intrinsic loss is significant, optimal coupling is no longer achieved by VCC but by a generalized matched-filter excitation. Third, we demonstrate that generalized VCC to a two-resonator chain enables an energy-efficient active optical delay beyond the delay-bandwidth limit. These results should prove useful in engineering integrated photonics systems for optical processes such as nonlinear wave mixing, adiabatic frequency tuning, optical buffering, optical synchronization, and quantum repeating.

In this paper, we investigate entanglement generation and optimization between two giant atoms coupled to a common one-dimensional waveguide. By introducing relative coupling phases between the connection points, we provide a unique approach to controlling quantum interference, which enables highly tunable decay dynamics of giant atoms into the waveguide. Within this framework, phase-dependent dark states can be precisely engineered to facilitate the spontaneous steady-state entanglement. For a single-excitation initial state, the maximum achievable entanglement exceeds the conventional upper bound of 0.5 for small atoms by $\sim 30\%$. Moreover, the system maintains strong steady-state entanglement even under double-excitation conditions, which is not attainable with small atoms. Furthermore, by employing coherent two-atom driving, highly entangled steady states with concurrence $C\approx 0.995$ can be achieved. The formation time is reduced by nearly two orders of magnitude compared to previous schemes, and no specific topology is required. Our results demonstrate the potential of giant atoms for quantum entanglement protocols and suggest promising applications in quantum information processing and large-scale quantum networks based on waveguide quantum electrodynamics.

A recent experiment demonstrated delayed superradiance from ${}^{88}\mathrm{Sr}$ atoms, which are coupled to a longitudinal mode of a cavity while being excited by a laser pulse propagating along a transversal direction [Nat. Commun. 15, 1084 (2024)]. A coherent picture of the atomic ensemble dynamics in this experiment requires complementary representations of the external driving dynamics and the superradiant dynamics. To complement previous analyses, we introduce these representations by considering in-phase and out-of-phase superpositions of transverse collective spin components of two atomic subensembles, and analyze the dynamics with the corresponding collective Dicke states and Bloch vectors. This approach also explains Ramsey spectroscopy experiments based on the delayed superradiance, and it may be employed to explore other intriguing phenomena, such as weak- to strong-coupling phase transitions and triggered superradiance.

Cold atom systems in optical lattices have long been recognized as an ideal platform for bridging condense matter physics and quantum optics. Here, we investigate the one-dimensional (1D) fermionic superradiance in an optical lattice, and uncover tricritical phenomena and multistability in finite-temperature cases. As a starting point, we compare the 1D and 2D Fermi gases in zero-temperature limit. It turns out that the tricritical point originates from the higher-order Fermi surface nesting and the infrared divergence in 1D systems, which is absent in 2D cases. For dissipative cavities, we obtain the stable phase diagram and observe a hysteresis-type evolution under quench dynamics. When extending to finite-temperature cases, we derive analytical expressions for the secosecond- and fourfourth-order Landau coefficients, matching the numerical phase diagrams well, and reveal two different trcritical behaviors, named as quantum- and classic-type tricritical points, respectively. In addition, we construct the dependence between the susceptibility and the temperature, giving a nontrivial scaling law ${lim}_{\mathrm{\Delta }T\to 0}\mathrm{\Delta }{B}_c\sim \mathrm{\Delta }{T}^{\nu }$ with $\nu >1$. This work provides an approach to understanding tricritical phenomena, multistability, and scaling rate of self-organized cold atoms.

We consider the qubit-qutrit model of self-contained quantum refrigerator and observe the quantum Mpemba effect in its cooling. In this system, the qutrit acts as the refrigerator while the qubit is to be cooled. The entire system is coupled to three bosonic heat baths, due to which the dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation. We investigate the Liouvillian that generates the dynamics of the system and find that it has a block-diagonal form. The dynamics of each element of the system's density matrix can be determined by solving the dynamical equation of the corresponding block that contains it. We find that the steady state belongs to the block containing only the diagonal elements in the energy basis. We numerically solve for the steady state and investigate the steady-state cooling over a significant region of the parameter space. Moreover, we demonstrate the quantum Mpemba effect in the refrigerator: A Mpemba state obtained by applying a unitary on the equilibrium state of the system reaches the steady state faster than the equilibrium state, despite the Mpemba state being initially further away from the steady state. The Mpemba state thus leads to an acceleration in cooling of the cold qubit. We also find that both local and global unitaries on the qubit-qutrit system can generate the Mpemba state. Finally, we study the effect of the system-bath couplings on the Mpemba effect.

Quantum Fisher information (QFI) quantifies the precision that nonrandom parameters can be estimated using quantum probes and unbiased estimators. We demonstrate that QFI, associated with a quantum displacement estimation, precisely sets the minimal estimation uncertainty in quantum random parameter estimation. We establish a general framework for bounding the minimal estimation uncertainty in Bayesian quantum metrology, providing tight lower limits, which systematically enable quantum generalizations of classical precision bounds. Our framework enables the tightening of existing quantum bounds, the development of bounds that exploit the physical properties of noisy systems in realistic and specific scenarios, and the derivation of exact results within a unified quantum nonrandom estimation approach.

We study phase synchronization in a driven two-level system coupled to a non-Markovian bosonic reservoir. The dynamics is described by treating the system-bath coupling and the coherent drive without invoking the rotating-wave approximation, and simulated using the numerically exact hierarchical equations of motion. We observe that a robust phase locking develops and that the corresponding synchronization measure rapidly acquires a finite value when the system is tuned to what we identify as a resonant-ratio condition, namely, when the ratio between the drive amplitude and its frequency coincides with a zero of the Bessel function $J_0$. We provide an explanation for this phenomenon by means of a static approximation derived from a Fourier analysis of the periodically driven Hamiltonian.

Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum computing. This work stresses that for translationally invariant lattice Hamiltonians with periodic boundary conditions, one can easily derive efficiently computable lower bounds to ground state energies that can and should be compared with variational principles providing upper bounds. As small technical results, it is shown that (i) the Anderson bound and a (ii) common hierarchy of semidefinite relaxations both provide approximations with performance guarantees that scale as a constant in the energy density for cubic lattices. (iii) Also, the Anderson bound is systematically improved as a hierarchy of semidefinite relaxations inspired by the quantum marginal problem.

We design flexible fault-tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to perform both Clifford and non-Clifford gates fault tolerantly on generic quantum codes, including both for stabilizer codes and, assuming the availability of suitable FT error-correction or measurement gadgets, for nonadditive codes. This allows us to demonstrate the first universal fault-tolerant gate set for nonadditive codes at the level of logical circuits. We consider fault tolerance with respect to both a dephasing channel and a depolarizing channel.

Measurements are central in all quantitative sciences, and a fundamental challenge is to make observations without systematic measurement errors. This holds in particular for quantum information processing, where other error sources, such as noise and decoherence, are unavoidable. Consequently, methods for detecting systematic errors have been developed, but the required quantum state properties are yet unexplored. We theoretically develop a direct and efficient method to detect systematic errors in quantum experiments and demonstrate it experimentally using quantum state tomography of photon pairs emitted from a semiconductor quantum dot. Our method can be scaled to multiqubit systems, and we find that entanglement and quantum states with high purity can help identify systematic errors.

Quantum algorithms have emerged as a promising tool to solve combinatorial optimization problems. The quantum walk optimization algorithm (QWOA) is one such variational approach that has recently gained attention. In the broader context of variational quantum algorithms, understanding the expressivity of the Ansatz has proven critical for evaluating their performance. A key method to study this aspect involves analyzing the dimension of the dynamic Lie algebra (DLA). In this work, we derive novel upper bounds on the DLA dimension for QWOA applied to arbitrary optimization problems. Specifically, we show that the DLA dimension scales at most quadratically with the number of distinct eigenvalues of the problem Hamiltonian. As a consequence, our bound guarantees a polynomial DLA dimension with respect to the input size for optimization problems in the class $\text{NPO}\text{−}\text{PB}$. This result, coupled with recently established performance bounds for QWOA, allows us to identify complexity-theoretic conditions under which QWOA must be overparameterized to obtain optimal or approximate solutions for $\text{NPO}\text{−}\text{PB}$ problems.

Hybrid quantum-classical models aim to harness the strengths of both quantum computing and classical machine learning, but their practical potential remains poorly understood. In this work, we develop a unified mathematical framework for analyzing generalization in hybrid models, offering insight into how these systems learn from data. We establish a generalization bound of the form $\tilde{\mathcal{O}}\left(\frac{{\alpha }^k}{\sqrt{N}}(k^{\frac{3}{2}}\sqrt{mn}+\sqrt{TlogT})\right)$ for $N$ training data points, $T$ trainable quantum gates, $n$-dimensional quantum circuit output, and $k$ bounded linear layers $\parallel F_i{\parallel }_F\le \alpha$, where $i=1,\cdots ,k$ and $F\in {\mathbb{R}}^{m\times n}$ interspersed with activation functions. This generalization bound decomposes into quantum and classical contributions, providing a theoretical framework to separate their influence and clarifying their interaction. Alongside the bound, we highlight conceptual limitations of applying classical statistical learning theory in the hybrid setting and suggest promising directions for future theoretical work.

Going beyond short-range interactions, we explore the role of long-range interactions in the extended $XY$ model for transferring quantum states through evolution. In particular, employing a spin-1/2 chain with interactions decaying as a power law, we demonstrate that long-range (LR) interactions significantly enhance the efficiency of a quantum state transfer (QST) protocol, improving the achievable fidelity, mitigating its slow decline as compared with the nearest-neighbor setting, associated with increasing system-size. Our study identifies the LR regime as providing an optimal balance between interaction range and transfer efficiency, outperforming the protocol with the short-range interacting model. Our detailed analysis reveals the impact of system parameters, such as anisotropy, magnetic field strength, and coordination number, on QST dynamics. Specifically, we find that intermediate coordination numbers lead to a faster and more reliable state transfer, while extreme values diminish performance. Furthermore, we exhibit that the presence of LR interactions considerably reduces the minimum time required to achieve fidelity beyond the classical limit.

Universal quantum gates whose operation depends on the manipulation of the geometric phase of atomic systems are promising candidates for implementation of quantum computing. We propose a scheme inducing a nontrivial Aharonov-Anandan geometric phase in pairs of atoms interacting via dipole-dipole potential. Our protocol relies on mobile optical trap technology and consists of steering a single atom along a closed loop. The trajectory of the atom is controlled by a mobile optical trap, and the shape of the path is designed by applying an optimal control procedure. The geometric phase is generated as a residual of the two-atom entanglement induced by the dipole-dipole interaction. The stability of our scheme in the presence of noise or experimental imperfections is discussed.