Several works on optical higher-order differential operations have recently attracted attention, particularly in image processing for edge detection. However, the inefficient differential operation leads to barriers to practical applications. Here, we report an anisotropic epsilon-near-zero slab to significantly enhance the transmission efficiency of second-order differentiators and discuss the Berry phase mechanism of this optical calculation process. Through a rigorous full-wave analysis of the process, we find that the conversion efficiency of differential operation depends on the spin-orbit interactions. Our scheme can strengthen the spin-orbit interaction by introducing anisotropy, which significantly enhances the transmission efficiency. We finally give transfer functions to reveal how to improve the efficiency and compare the quadratic coefficient among different systems. This highly efficient differentiation operation may develop significant applications in fast, compatible, and power-efficient ultrathin devices for data processing and biological imaging.

We design and demonstrate a technique for the active stabilization of the relative phase between seed and pump in an optical parametric oscillator (OPO). We show that two error signals for the stabilization of the OPO frequency, based on Pound-Drever-Hall (PDH), and of the seed-pump relative phase can be obtained just from the reflected beam of the OPO cavity, without the necessity of two different modulation and demodulation stages. We also analyze the effect of the pump in the cavity stabilization for different seed-pump relative phase configurations, resulting in an offset in the PDH error signal, which has to be compensated. Finally, an application of our technique in the reliable generation of squeezed coherent states is presented.

Single photons are at the heart of quantum information processing. The tasks of generating and storing single photons with arbitrary wave-packet shapes are crucial for building quantum networks, but they remain challenging. Here, we present a general machine learning (ML) algorithm with a self-adaptive process to optimize the control of a cavity-atom system for these tasks. This ML algorithm shows high efficiency and fidelity for both generation and storage of single photons. This ML-enhanced single-photon interface may pave the way for building flexible and reliable quantum networks because this ML algorithm can automatically adjust the quantum system according to single-photon wave functions in an “intelligent” way.

State preparation is of fundamental importance in quantum physics, which can be realized by constructing the quantum circuit as a unitary that transforms the initial state to the target, or implementing a quantum control protocol to evolve to the target state with a designed Hamiltonian. In this article, we study the latter on quantum many-body systems by time evolution with fixed couplings and variational magnetic fields. Specifically, we consider preparing the ground states of the Hamiltonians containing certain interactions that are missing in the Hamiltonians for the time evolution. An optimization method is proposed to optimize the magnetic fields by “fine graining” the discretization of time, in order to gain high precision and stability. The automatic differentiation technique is utilized to obtain the gradients of the fields against the logarithmic fidelity. Our method is tested on preparing the ground state of the Heisenberg chain with the time evolution by the $XY$ and Ising interactions, and its performance surpasses two baseline methods that use local and global optimization strategies, respectively. Our work can be applied and generalized to other quantum models such as those defined on higher-dimensional lattices. It enlightens to reduce the complexity of the required interactions for implementing quantum control or other tasks in quantum information and computation by means of optimizing the magnetic fields.

Non-Gaussian operations in continuous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis, and subtraction on squeezed coherent states on CV measurement-device-independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we observe that zero photon catalysis on the two-mode squeezed coherent state (TMSC) is an optimal choice for CV MDI QKD, while single photon subtraction is also a good candidate; both of them offer nearly 70 km of transmission distances. We also derive a single generalized covariance matrix for the aforementioned states which will be useful in several other aspects of CV quantum information processing.

Quantum hashing is a promising generalization of the cryptographic hashing concept on the quantum domain. In this paper, we construct a quantum hash via a sequence of single-photon states and perform a proof-of-principle experiment using orbital angular momentum (OAM) encoding. We experimentally verify the collision resistance of the quantum hash function depending on the number of qubits in use. Based on these results, we conclude that theoretical estimates are confirmed for different bases of OAM states and the proposed technique can be useful in computational and cryptographic scenarios. The possibility of multiplexing different OAM bases can make this approach even more efficient.

We study the polarization properties of elastic electron scattering on H-like ions using the relativistic QED theory. We calculate the complete set of parameters which describe the scattering of a polarized electron on an initially unpolarized ion and analyze them for both nonresonant and resonant scattering focusing on the LL-shell resonances. The study is carried out for ${\mathrm{B}}^{4+}, {\mathrm{Ca}}^{19+}, {\mathrm{Kr}}^{35+}$, and ${\mathrm{Xe}}^{53+}$ ions. We demonstrate that for the resonant electron scattering on ions with $Z$ up to 50 both the relativistic spin-orbit and the exchange interaction are equally significant. The possible spin exchange between the incident and bound electrons can fundamentally change the polarization of the scattered electron. We show that the involvement of the autoionizing states leads to quantitative and qualitative changes in the polarization parameters, in particular, to a significant increase in the spin asymmetry.

Revivals of initial nonequilibrium states is an ever-present concern for the theory of dynamic thermalization in many-body quantum systems. Here we consider a nonintegrable lattice of interacting spins 1/2 and show how to construct a quantum state such that a given spin 1/2 is maximally polarized initially and then exhibits an almost complete recovery of the initial polarization at a predetermined moment of time. An experimental observation of such revivals may be utilized to benchmark quantum simulators with a measurement of only one local observable. We further propose to utilize these revivals for a delayed disclosure of a secret.

We introduce the class of genuinely local operations and shared randomness multipartite nonlocal correlations, that is, correlations between $N$ parties that cannot be obtained from unlimited shared randomness supplemented by any composition of $(N-1)$-shared causal generalized probabilistic theory (GPT) resources. We then show that noisy $N$-partite Greenberger-Horne-Zeilinger (GHZ) quantum states as well as the three-partite $W$ quantum state can produce such correlations. This proves, if the operational predictions of quantum theory are correct, that nature's nonlocality must be boundlessly multipartite in any causal GPT. We develop a computational method which certifies that a noisy $N=3$ GHZ quantum state with fidelity $85\%$ satisfies this property, making an experimental demonstration of our results within reach. We provide our definition and contrast it with preexisting notions of genuine multipartite nonlocality. This work extends a more compact parallel Letter [X. Coiteux-Roy et al., No Bipartite-Nonlocal Causal Theory Can Explain Nature's Correlations, Phys. Rev. Lett. 127, 200401 (2021)] on the same subject and provides all the required technical proofs.

Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often intractable within a reasonable computation time, even when using supercomputers. To overcome the inherent limit of classical computing, we present a variational quantum algorithm for solving the Poisson equation that can be implemented in noisy intermediate-scale quantum devices. The proposed method defines the total potential energy of the Poisson equation as an expectation of certain observables, which are decomposed into a linear combination of Pauli operators and simple observables. The expectation value of these observables is then minimized with respect to a parameterized quantum state. Because the number of decomposed terms is independent of the size of the problem, this method requires relatively few quantum measurements. Numerical experiments demonstrate the faster computing speed of this method compared with classical computing methods and a previous variational quantum approach. We believe that our approach brings quantum computer-aided techniques closer to future applications in engineering developments.

Inspired by random walks on graphs, the diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional data set. In recent years, among its many applications, the DM has been successfully applied to discover relevant order parameters in many-body systems, enabling automatic classification of quantum phases of matter. However, a classical DM algorithm is computationally prohibitive for a large data set, and any reduction of the time complexity would be desirable. With a quantum computational speedup in mind, we propose a quantum algorithm for the DM, termed the quantum diffusion map (qDM). Our qDM takes as an input $N$ classical data vectors, performs an eigendecomposition of the Markov transition matrix in time $O\left({log}^{3}N\right)$, and classically constructs the diffusion map via the readout (tomography) of the eigenvectors, giving a total expected runtime proportional to $N^2\text{polylog}N$. Finally, quantum subroutines in the qDM for constructing a Markov transition matrix and for analyzing its spectral properties can also be useful for other random-walk-based algorithms.

In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove the quantum limit rigorously by infinite-dimensional analysis. A key to the proof is the choice of an unfavorable parametric submodel to give a bound for the semiparametric problem. By generalizing the quantum limit for a larger class of moments, I also prove that the measurement method of spatial-mode demultiplexing with just one or two modes is able to achieve the quantum limit. For comparison, I derive a classical bound for direct imaging using the parametric-submodel approach, which suggests that direct imaging is substantially inferior.

We address the use of neural networks (NNs) in classifying the environmental parameters of single-qubit dephasing channels. In particular, we investigate the performance of linear perceptrons and of two nonlinear NN architectures. At variance with time-series-based approaches, our goal is to learn a discretized probability distribution over the parameters using tomographic data at just two random instants of time. We consider dephasing channels originating either from classical $1/f^{\alpha }$ noise or from the interaction with a bath of quantum oscillators. The parameters to be classified are the color $\alpha$ of the classical noise or the Ohmicity parameter $s$ of the quantum environment. In both cases, we find that NNs are able to exactly classify parameters into 16 classes using noiseless data (a linear NN is enough for the color, whereas a single-layer NN is needed for the Ohmicity). In the presence of noisy data (e.g., coming from noisy tomographic measurements), the network is able to classify the color of the $1/f^{\alpha }$ noise into 16 classes with about $70\%$ accuracy, whereas classification of Ohmicity turns out to be challenging. We also consider a more coarse-grained task and train the network to discriminate between two macroclasses corresponding to $\alpha \lessgtr 1$ and $s\lessgtr 1$, obtaining up to $96\%$ and $79\%$ accuracy using single-layer NNs.

We analyze a scheme for generating multiphoton entangled states by a single solid-state quantum emitter and devise a mathematical framework for assessing the fidelity of the generated state. Within this formalism, we theoretically study the role of imperfections present in real systems on the generation of time-bin encoded Greenberger–Horne–Zeilinger and one-dimensional cluster states. We consider both fundamental limitations, such as the effect of phonon-induced dephasing, interaction with the nuclear spin bath, and second-order emissions, as well as technological imperfections, such as branching effects, nonperfect filtering, and photon losses. The devised framework is applicable to a range of quantum emitters, including semiconductor quantum dots, defect centers in solids, and atoms in cavities.

The precision of the photoassociation spectroscopy of the Yb dimer in degenerate gases is enough to improve the constraints on short-range gravitylike forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [Borkowski et al., Sci. Rep. 9, 14807 (2019)]. The ground-state interaction potential of the ytterbium dimer is investigated at the exact two-component core-correlated coupled-cluster method with singles, doubles, and noniterative triples [CCSD(T)] level of ab initio theory in the complete-basis-set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. The empirical constraint on the number of bound vibrational energy levels of the ${}^{174}\mathrm{Yb}_2$ dimer is accounted for by representing the global ab initio–based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on short-range gravitylike forces by ultracold atomic spectroscopy.

We present a model that unifies Gaussian wave-packet evolution with the so-called “time-dependent Thomas-Fermi approximation” for a Bose-Einstein condensate (BEC) of strongly interacting atoms. The unified simple intuitive formalism describes the stationary or time-dependent properties of single atoms, thermal clouds, or a BEC over a wide range of interaction strengths, including intermediate interaction regimes or scenarios where both interaction regimes coexist. Excellent agreement with precise numerical calculations (Gross-Pitaevskii equations) is obtained. The model is particularly suitable for describing three-dimensional evolution in free space or in time-dependent potentials for trapping, guiding, accelerating, focusing, or splitting matter waves in interferometers. We present a unified theory of spatial coherence in matter-wave interferometers and find good agreement between analytical expressions for the evolution of the coherence length of thermal atoms or a BEC and precise numerical calculations. In addition to the insight provided by the model, it supplies a simple and useful tool for the design and performance analysis of atom interferometers with many operational parameters, where a precise numerical calculation might exhaust unrealistic calculational resources.

We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.

Standard optical potentials use an off-resonant laser standing-wave-induced ac Stark shift. In a recent development [Łącki et al., Phys. Rev. Lett. 117, 233001 (2016)] a three-level scheme in a $\mathrm{\Lambda }$ configuration coupled coherently by resonant laser fields was introduced, leading to an effective lattice with subwavelength potential peaks. Here, as an extension of that work, a four-level atomic setup in the tripod configuration is used to create spin-$\frac{1}{2}$-like two-dimensional dark space with one-dimensional motion and the presence of external gauge fields. Most interestingly for possible applications, the lifetime for a dark subspace motion is up to two orders of magnitude longer than for a similar $\mathrm{\Lambda }$ system. The model is quite flexible, leading to lattices with significant nearest, next-nearest, or next-to-next-nearest hopping amplitudes $J_1, J_2$, and $J_3$ offering intriguing possibilities to study, e.g., frustrated systems. The characteristic Wannier functions lead also to a type of intersite interaction not realizable in typical optical lattices.