The Goos-Hänchen (GH) effect, a fundamental beam displacement phenomenon occurring during total internal reflection, has been challenging to utilize directly in high-sensitivity applications due to its inherently small, subwavelength scale. The weak measurements have been widely used to amplify this effect involving abstruse quantum interpretations. In this work, we present a clear and insightful classical wave-optics derivation and visualization of the weak-measurement amplification process for the GH effect from the perspective of optical differential interference. By leveraging the polarization-dependent lateral displacements induced by the GH effect, we demonstrate that the reflected field can be decomposed into a fundamental Gaussian component and a first-order differential component. Through coherent superposition using a simple polarizer, we establish an interferometric setup that directly converts the nanometer-scale GH shift into a micrometer-scale displacement of the output field centroid. Our model, derived entirely from classical electromagnetic theory and Fourier optics, provides a clear physical picture of the amplification mechanism. This work offers a versatile and powerful framework for precision measurement, nanophotonics, and interferometric sensing.

Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce the hypothesis space. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that (i) the sources distribute the same physical systems, (ii) these physical systems respect relativistic causality, and (iii) the correlations are the observed ones are incompatible.

We explore the decomposition of ergotropy into incoherent and coherent parts for quantum systems exposed to typical Markovian noise channels. The incoherent contribution arises from population inversion in the energy eigenbasis after dephasing, while the coherent contribution reflects the impact of quantum coherence on work extraction. For single-qubit systems, we derive explicit conditions for freezing and even enhancement of the coherent work and establish an analytical upper bound, showing that the coherent contribution cannot exceed one-half of the state’s quantum coherence. We then analyze two distinct classes of separable two-qubit states, where both qubits are affected by noise. For Bell-diagonal states—locally completely passive and therefore lacking local coherence—we prove a theorem establishing that the total extractable work under noise equals the average of the geometric quantum and classical correlations. In this case, no enhancement of coherent ergotropy occurs, although specific freezing behavior is identified under certain noise conditions. In contrast, for separable states endowed with local coherence, coherent ergotropy can increase under all investigated noises, even phase flip and depolarizing channels that are typically expected to destroy coherence. Extending to multipartite systems, we find that both the magnitude and the range of noise-induced enhancement scale with the number of qubits, revealing a collective reinforcement of the coherent ergotropy. Finally, we show by means of an explicit example that entanglement does not preclude this enhancement, and that coherent ergotropy can increase under noise even for entangled states. These findings provide novel insights into how noise can be leveraged in quantum systems for energy storage, contrary to the conventional perspective, suggesting that noise-assisted enhancement of stored energy can coexist with fast-charging mechanisms typically enabled by entangling operations in quantum batteries.

The variational quantum eigensolver (VQE) is a hybrid quantum-classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the reach of classical brute-force simulation, it is important to assess the quality of solutions produced by them. Here we propose a dual variational quantum eigensolver (dual-VQE) that produces a lower-bound estimate of the ground-state energy. As such, VQE and dual-VQE can serve as quality checks on their solutions; in the ideal case the VQE upper bound and the dual-VQE lower bound form an interval containing the true optimal value of the ground-state energy. The idea behind dual-VQE is to employ semidefinite programming duality to rewrite the ground-state optimization problem as a constrained maximization problem, which itself can be bounded from below by an unconstrained optimization problem to be solved by a variational quantum algorithm. When using a convex combination ansatz in conjunction with a classical generative model, the quantum computational resources needed to evaluate the objective function of dual-VQE are no greater than those needed for that of VQE. We also show that the problem is well suited for classical pretraining using matrix product states and these methods help warm-start the optimization. We simulated the performance of dual-VQE on the transverse-field Ising model with and without pretraining and found that, for the example considered, while dual-VQE training is slower and noisier than VQE, it approaches the true value with an error of order ${10}^{-2}$.

Key quantum features like coherence are the fundamental resources enabling quantum advantages and ascertaining their presence in quantum systems is crucial for developing quantum technologies. This task, however, faces severe challenges in the noisy intermediate-scale quantum era. On one hand, experimental data are typically scarce, rendering full state reconstruction infeasible. On the other hand, these features are usually quantified by highly nonlinear functionals that elude efficient estimations via existing methods. In this work, we propose a scalable protocol for estimating coherence from scarce data and further experimentally demonstrate its practical utility. The key innovation here is to relax the potentially NP-hard coherence estimation problem into a computationally efficient optimization. This renders the computational cost in our protocol insensitive to the system size, in sharp contrast to the exponential growth in traditional methods. This work opens a route toward estimating coherence of large-scale quantum systems under data-scarce conditions.

Estimating quantum state purity is a key task for assessing decoherence and state-preparation fidelity in quantum experiments, yet full tomography becomes infeasible for large systems. We consider the problem of estimating the purities of multiple unknown quantum states using Pauli measurements, where each Pauli basis can be employed for up to $M$ measurements in total. In this setting, the central challenge is to allocate the limited measurement resources efficiently to enhance overall estimation precision. We propose an adaptive allocation strategy that dynamically redistributes measurements according to observed outcomes. Theoretically, our method achieves a worst-case error scaling of $O\left(M^{-3/2}\right)$, outperforming nonadaptive approaches limited to $O\left(M^{-1}\right)$. Numerical simulations confirm the predicted scaling and robustness across different state ensembles. These results establish an efficient and scalable framework for multistate purity estimation, with direct relevance to quantum property learning and noise characterization in noisy intermediate-scale quantum devices.

Fast and accurate quantum gates and measurements are essential for quantum computation within the limited coherence time of superconducting qubits. A quantum nondemolition (QND) readout is typically achieved through the dispersive interaction with a readout resonator. The reduction in the readout time required for qubit-state discrimination can be achieved through careful device designs, optimization of readout parameters, and the use of quantum-limited amplifiers. However, the transient response in the readout signal can degrade the readout fidelity, particularly during fast measurements. In this work, we propose enhancing readout fidelity and shortening readout time by systematically discarding the transient response. We numerically demonstrate that, with an optimal ratio between the dispersive shift and the photon decay rate, the effective readout time can be reduced by approximately $6\%\text{–}9\%$ for square pulses and $10\%\text{–}16\%$ for Gaussian pulses, while maintaining the same fidelity for the quantum efficiency $0.5\le \eta \le 1$.

We propose a blockchain architecture in which mining requires a quantum computer. The consensus mechanism is based on proof of quantum work, a quantum-enhanced alternative to traditional proof of work that leverages beyond-classical quantum computation to make mining intractable for classical computers. We have refined the blockchain framework to incorporate the probabilistic nature of quantum mechanics, ensuring stability against sampling errors and hardware inaccuracies. To validate our approach, we implemented a prototype blockchain on four ${\text{D-Wave}}^{\mathrm{TM}}$ quantum annealing processors geographically distributed within North America, demonstrating stable operation across hundreds of thousands of quantum hashing operations. Our sampling protocol follows the same approach used in the recent demonstration of beyond-classical computation [Andrew D. King, et al, Beyond-classical computation in quantum simulation, Science 388, 199 (2025)], ensuring that classical computers cannot efficiently perform the same computation task. By replacing classical machines with quantum systems for mining, it is possible to significantly reduce the energy consumption and environmental impact traditionally associated with blockchain mining while providing a quantum-safe layer of security. Beyond serving as a proof of concept for a meaningful application of quantum computing, this work highlights the potential for other near-term quantum computing applications using existing technology.

High-fidelity qubit readout is a fundamental requirement for practical quantum computing systems. In this work, we investigate methods to enhance the measurement fidelity of flux qubits via a quantum flux parametron-mediated readout scheme. Through theoretical modeling and numerical simulations, we analyze the impact of different measurement bases on fidelity in single-qubit and coupled two-qubit systems. For single-qubit systems, we show that energy bases consistently outperform flux bases in achieving higher fidelity. In coupled two-qubit systems, we explore two measurement models: sequential and simultaneous measurements, both aimed at reading out a single target qubit. Our results indicate that the highest fidelity can be achieved either by performing sequential measurement in a dressed basis over a longer duration or by conducting simultaneous measurement in a bare basis over a shorter duration. Importantly, the sequential measurement model consistently yields more robust and higher-fidelity readouts compared to the simultaneous approach. These findings quantify achievable fidelities and provide valuable guidance for optimizing measurement protocols in emerging quantum computing architectures.

We demonstrate the implementation of $\mathrm{\Lambda }$-enhanced gray molasses cooling on the $D_2$ line of ${}^{85}\mathrm{Rb}$ atoms in an optical tweezer array. This technique yields lower atomic temperatures of 4.0(2) µK compared with red-detuned polarization gradient cooling, and consequently extends the $T_2^{*}$ coherence time of the hyperfine clock qubit by a factor of 1.5. The method is alignment-free and can be readily implemented on laser beams used for magneto-optical trapping because it only requires frequency and phase modulation control. Our experimental observations are corroborated by a numerical model based on a semiclassical force approach extended to a four-level system, including two hyperfine states of the upper manifold that are $120\mathrm{M}\mathrm{Hz}$ apart.

Motivated by recent breakthrough studies of wave hyperbolicity in extremely anisotropic natural materials and artificial composites, we investigate the radiation pattern of a localized emitter in a hyperbolic medium. Since the emission of a point source is associated with the Fourier transform of the isofrequency contour of a medium, we derive and analyze the properties of the Fourier transform of hyperbolic dispersion, which provides insight into the emission properties in the presence of hyperbolic bands. Our analysis leads to a generalized form of Huygens' principle for hyperbolic waves, connecting to the emergence of negative refraction and focusing with hyperbolic media. We also highlight the occurrence of aliasing artifacts in polariton imaging. More broadly, our findings provide analytical tools to model polariton propagation in materials with extreme anisotropy and may be applied to several other physical platforms featuring hyperbolic responses, from astrophysics to seismology.

We report on the observation of intensity squeezing based in four-wave mixing (FWM) on a pure two-level system. We employ a two-mode probe beam, where the two probe modes play a double role, either for generating the forward-FWM beams as well as a reference interfering beam. The technique relies on the phase conjugation property associated with the generated forward-FWM. Using a cold ensemble of cesium atoms and a pump beam red-detuned by 30 MHz from resonance of the closed transition $6S_{1/2},F=4,m_F=4\to 6P_{3/2},F^{\prime }=5,m_{F^{\prime }}=5$, we have demonstrated directly the production of of light intensity squeezing. Possible extension of the present technique is also discussed for FWM processes involving more complex atomic-level schemes.

Quantum state tomography is a fundamental technique in quantum information science for reconstructing the density matrix of an unknown quantum state, thereby providing complete information about the state. It plays a crucial role in quantum computation, quantum communication, and quantum simulation. However, as the size of the quantum system increases, the number of measurement settings and sampling requirements for quantum state tomography grow exponentially with the number of qubits. This not only complicates experimental design and implementation but also leads to substantial consumption of experimental resources. These limitations significantly hinder the application of state tomography in large-scale quantum systems. To reduce the number of measurement settings and improve sampling efficiency, this study proposes a tomography method based on auxiliary systems. The method can be implemented either through entanglement between the quantum system to be measured and a quantum auxiliary system or through correlations between the quantum system and a probabilistic classical auxiliary system. Measurements performed on the joint system enable more efficient extraction of information about the target quantum state. The method relies on standard quantum gate operations and requires only two measurement settings, with a total sampling complexity scaling as $O\left(d^2\right)$ for the system of interest with $d$ dimensions, significantly simplifying experimental operations and measurement processes. Additionally, this study provides two schemes for purity estimation based on the proposed circuit, one of which achieves estimation precision at the Heisenberg limit. The effectiveness of the proposed method is validated through detailed theoretical analysis, numerical simulations, and cloud-based quantum computing demonstrations.

The joint state of a continuously monitored quantum system and the classical filtered measurement record has recently been shown to be described by a quantum Fokker-Planck master equation [Phys. Rev. Lett. 129, 050401 (2022)]. We present a deterministic approach to compute the steady state of the system and detector. The method is shown to become particularly efficient in the absence of feedback, which we exploit to develop a perturbative approach valid for weak feedback. We show that through this method we can extract the full counting statistics of the signal, the quantum-classical mutual information between the system and signal, and the Fisher information of the signal, which can be used for sensing applications. Our results are illustrated with both single-qubit models and the spin chains governed by the one-dimensional transverse field Ising model or the Lipkin-Meshkov-Glick model.

We develop a theoretical framework to interpret “bump-like” enhancements in the energy distribution of electrons emitted from cesium atoms subjected to intense infrared laser fields, as observed in a recent experiment. These emissions, detected at energies approaching twice the ponderomotive energy ($2U_{\text{p}}$), indicate a mechanism where electrons are nonadiabatically ejected with substantial inward velocity following ionization. The bump-like features arise from returning trajectories that scatter off the residual ion. We interpret these experimental results classically using a periodically driven version of the Bohr model and quantum mechanically through Keldysh's adiabaticity parameter (${\gamma }_{\text{K}}$) and Reiss's continuum-state intensity parameter $\mathcal{Z}$ in a Coulomb-corrected version of the strong-field approximation (SFA) that incorporates “complex” electronic trajectories. Notably, our theoretical analysis shows that these emissions are independent of the specific short-range form of the atomic potential.

We study the resonance-enhanced multiphoton ionization (REMPI) of atoms by intense, short, XUV radiation fields. To characterize Rabi oscillations and the resulting Autler-Townes doublet in the photoelectron spectrum, a minimal-state effective description is utilized, incorporating energy-level shifts, multiphoton couplings, and irreversible losses. Extending the semiclassical Rabi model with such higher-order terms, the complex population amplitudes of the Rabi cycling atom are found in simple analytic forms. This allows for the exact analytic evaluation of the photoelectron spectrum under various simultaneous physical effects. The origins of the spectral characteristics, such as the splitting, shifting, asymmetry, and multipeak pattern, are identified through the found spectrum formula. Furthermore, the dependence of these features on the field intensity, frequency detuning, and interaction time are analyzed in detail. Finally, as the simplicity of the spectrum formula is preserved when further higher-order light-matter interaction terms are added, the presented general framework is suitable for studying arbitrary ($n+m$) photon REMPI phenomena.

Cold atoms in optical lattices are a versatile and highly controllable platform for quantum simulation, capable of realizing a broad family of Hubbard models, and allowing site-resolved readout via quantum gas microscopes. In principle, arbitrary site-dependent potentials can also be implemented; however, since lattice spacings are typically below the diffraction limit, precisely applying and calibrating these potentials remains challenging. Here, we propose a simple and efficient experimental protocol that can be used to measure any potential with high precision. The key ingredient in our protocol is the ability in some atomic species to turn off interactions using a Feshbach resonance, which makes the evolution easy to compute. Given this, we demonstrate that collecting snapshots from the time evolution of a known, easily prepared initial state is sufficient to accurately estimate the potential. Our protocol is robust to state-preparation errors and uncertainty in the hopping rate. This paves the way toward precision quantum simulation with arbitrary potentials.

The use of quantum light to probe exciton properties in semiconductor and molecular nanostructures typically occurs in the low-intensity regime. A substantial enhancement of exciton-photon coupling can be achieved with photonic cavities, where excitons hybridize with cavity modes to form polariton states. To provide a theoretical framework for interpreting emerging experimental efforts in this direction, we develop a scattering theory describing the interaction of frequency-entangled photon pairs with cavity polariton and bipolariton states under various coupling regimes. Employing the Tavis-Cummings model in combination with our scattering approach, we present a quantitative analysis of how the interaction of the entangled photon pair with the polariton or bipolariton modifies its joint spectral amplitude (JSA). Specifically, we examine the effects of the cavity-mode steady-state population, exciton-cavity coupling strength, and different forms of the input photon JSA. Our results show that the entanglement entropy of the scattered photons is highly sensitive to the interplay between the input JSA and the spectral line shapes of the polariton resonances, emphasizing the cavity filtering effects. We suggest that biphoton-scattering quantum light spectroscopy best serves as a sensitive probe of polariton and bipolariton states in the photon-vacuum cavity state. Our approach is not only robust to various regimes of cavity-exciton coupling, but also amenable to extensions beyond the Tavis-Cummings model, enabling the representation of a broad class of molecular systems and solid state quantum materials.