The spin angular-momentum density vector and the so-called spin vector reflecting the polarization properties of a light field are parallel for a monochromatic light field whose polarization ellipse at a point necessarily lies in a fixed plane. In contrast, the electric field of polychromatic light may, in general, evolve in three directions such that the average intensity in all of them is nonzero for any orientation of the reference frame. Consequently, the two vectors are no longer necessarily parallel. In this work we consider tightly focused bichromatic Lissajous beams and show that the spin angular-momentum density vector and the spin vector in such three-dimensional light fields may point in markedly different directions, almost orthogonal in some cases, and thus generally provide different information on the spin of light.

Entangled photons (biphotons) in the time-frequency degree of freedom play a crucial role in both foundational physics and advanced quantum technologies. Fully characterizing them poses a key scientific challenge. Here, we propose a theoretical approach to achieving the complete tomography of biphotons by introducing a frequency shift in one arm of the combination interferometer. Our method, a generalized combination interferometer, enables the reconstruction of the full complex joint spectral amplitude associated with both frequency sum and difference in a single interferometer. In contrast, the generalized Hong-Ou-Mandel and N00N state interferometers only allow for the partial tomography of biphotons, either in frequency difference or frequency sum. This provides an alternative method for full characterization of an arbitrary two-photon state with exchange symmetry and holds potential for applications in high-dimensional quantum information processing.

An approximate quantum state preparation method is introduced, called the Walsh series loader (WSL). The WSL approximates quantum states defined by real-value functions of single real variables with a depth independent of the number $n$ of qubits. Two approaches are presented. The first one approximates the target quantum state by a Walsh series truncated at $O(1/\sqrt{\epsilon })$, where $\epsilon$ is the precision of the approximation in terms of infidelity. The circuit depth is also $O(1/\sqrt{\epsilon })$, the size is $O(n+1/\sqrt{\epsilon })$, and only one ancilla qubit is needed. The second method accurately represents quantum states with sparse Walsh series. The WSL loads $s$-sparse Walsh series into $n$ qubits with a depth doubly sparse in $s$ and $k$, the maximum number of bits with value 1 in the binary decomposition of the Walsh function indices. The associated quantum circuit approximates the sparse Walsh series up to an error $\epsilon$ with a depth $O\left(sk\right)$, a size $O(n+sk)$, and one ancilla qubit. In both cases, the protocol is a repeat-until-success procedure with a probability of success $P=\mathrm{\Theta }\left(\epsilon \right)$, giving an averaged total time of $O(1/{\epsilon }^{3/2})$ for the WSL and $O(sk/\epsilon )$ for the sparse WSL. Amplitude amplification can be used to reach a probability of success $P=\mathrm{\Theta }\left(1\right)$, modifying the quantum circuit size to $\tilde{O}((n+1/\sqrt{\epsilon })/\sqrt{\epsilon })$ and $\tilde{O}((n+sk)/\sqrt{\epsilon })$ and the depth to $O([log{\left(n\right)}^3+1/\sqrt{\epsilon }]/\sqrt{\epsilon })$ and $O([log{\left(n\right)}^3+sk]/\sqrt{\epsilon })$, respectively. Amplitude amplification reduces by a factor $O(1/\sqrt{\epsilon })$ the total time dependence on $\epsilon$ but increases the size and depth of the associated quantum circuits, making them linearly dependent on $n$. These protocols give overall efficient algorithms with no exponential scaling in any parameter. They can be generalized to any complex-value, multivariate, almost-everywhere-differentiable function. The repeat-until-success Walsh series loader is so far the only method that prepares a quantum state with a circuit depth and an averaged total time independent of the number of qubits.

We introduce entanglement witnesses for spin ensembles which detect genuine multipartite entanglement using only measurements of the total angular momentum. States that are missed by most other angular-momentum-based witnesses for spin ensembles, which include Greenberger-Horne-Zeilinger states and certain superpositions of Dicke states, can be effectively detected by our witness. The protocol involves estimating the probability that the total angular momentum is positive along equally spaced directions on a plane. Alternatively, one could measure along a single direction at different times, under the assumption that the total spins undergo a uniform precession. Genuine multipartite entanglement is detected when the observed score exceeds a separable bound. Exact analytical expressions for the separable bound are obtained for spin ensembles $j_1\otimes j_2\otimes \cdots \otimes j_N$ such that the total spin is a half-integer and numerical results are reported for the other cases. Finally, we conjecture an expression for the separable bound when the total spin is not known, which is well supported by the numerical results.

Diagonal unitary operators are well known to be key building blocks of many quantum algorithms and quantum computing procedures, and thus resource-efficient quantum circuit implementations are in demand. Here we propose a constructive algorithm that can generate a quantum circuit over the primitive gate set {cnot, $R_Z$} for realizing any given diagonal unitary operator piece by piece. The theoretical analysis reveals that, for the general case, our generated circuit not only ensures the asymptotically optimal gate count, but also nearly halves the circuit depth compared with the previous Welch's method [New J. Phys. 16, 033040 (2014)]. Specifically, this substantial depth optimization originates from the use of a uniform circuit rewriting rule developed here. The performance of our circuit synthesis algorithm is further validated by numerical evaluations on two examples. First, we achieve a nearly 50% depth reduction over Welch's method for synthesizing random diagonal unitary operators with up to 16 qubits. Second, we achieve an average of 22.05% depth reduction for resynthesizing the diagonal part of the specific quantum approximate optimization algorithm (QAOA) circuits with up to 14 qubits.

Weak measurement has been proven to amplify the detection of changes in meters while discarding most photons due to the low probability of postselection. Previous power-recycling schemes enable the failed postselection photons to be repeatedly selected, thus overcoming the inefficient postselection and increasing the precision of detection. In this study, we focus on the polarization-based weak value angular-velocity measurement and introduce three cyclic methods to enhance the accuracy of detecting time shifts in a Gaussian beam: power-recycling, signal-recycling, and dual-recycling schemes. By incorporating one or two partially transmitting mirrors into the system, both the power and the signal-to-noise ratio of the detected light are substantially enhanced. Compared to nonpolarization schemes, polarization-based approaches offer several advantages, including lower optical loss, unique cyclic directions, and a wider optimal region. These features effectively reduce crosstalk among different light paths and theoretically eliminate the walk-off effect, thus yielding improvements in both theoretical performance and application.

Real-world Bennett-Brassard 1984 quantum key distribution (QKD) systems utilize imperfect devices that introduce vulnerabilities to their security, known as side-channel attacks. Measurement-device-independent (MDI) QKD authorizes an untrusted third party to make measurements and removes all side-channel attacks. The typical implementations of MDI QKD employ nearly symmetric channels which are difficult to realize physically in many practical scenarios such as when asymmetric channel losses are present, normally a consequence of the communication environment. Maritime and satellite-based communications are two such instances in which the channels are characterized by continuously changing losses in different channels. In this work we perform asymmetric MDI QKD in a laboratory environment with simulated turbulence using an acousto-optic modulator to interrogate the performance of free-space quantum communication. Under turbulent conditions, scattering and beam wandering cause intensity fluctuations which decrease the detected signal-to-noise ratio. Using the seven-intensity optimization method proposed by Wang et al. [Phys. Rev. X 9, 041012 (2019)], coupled with prefixed-threshold real-time selection (PRTS), we demonstrate enhancement in the secure key rate under turbulent conditions for finite-size decoy-state MDI QKD. Furthermore, we show that PRTS can yield higher secure key rates, particularly in the high-loss regime.

Graph states possess significant practical value in measurement-based quantum computation, with complete graph states that exhibit exceptional performance in quantum metrology. In this work, we introduce a method for generating multiparticle complete graph states using a spin-$1/2$ Heisenberg $XX$ chain subjected to a time-varying magnetic field, which applies to a wide range of systems. Our scheme relies exclusively on nearest-neighbor interactions between atoms, with real-time magnetic field formation facilitated by quantum optimal control theory. We focus specifically on neutral-atom systems, finding that multiparticle complete graph states with $N=3–6$ can be achieved in less than $0.25\mu \mathrm{s}$, using a hopping amplitude of $J/\left(2\pi \right)=-2.443\mathrm{MHz}$. This assumes an initial state provided by an equal-weight superposition of all spin states that are encoded by the dipolar-interacting Rydberg states. Furthermore, we thoroughly address various experimental imperfections and showcase the robustness of our approach against atomic vibrations, fluctuations in pulse amplitude, and spontaneous emission of Rydberg states. Taking into account the common occurrence of disturbances in the experimental setups of neutral-atom systems, our one-step strategy to achieve such graph states emerges as a viable alternative to techniques based on controlled-$Z$ gates.

A theoretical investigation is conducted on the $s$- and $p$-wave elastic scatterings of positronium by a lithium ion ${\text{Li}}^{+}$ with the scattering energy below 1.41 eV, corresponding to the threshold of the $e^{+}$-Li channel. The confined variational method is applied to serve as the theoretical framework for this study. To accurately account for correlations between involved particles, explicitly correlated Gaussians are employed as basis functions, which are optimized through a hybrid approach combining stochastic variational and energy-gradient-based methods. Additionally, a straightforward yet effective algorithm is developed for the automatic adjustment of confining potentials. The $s$-wave zero-energy pickoff annihilation parameter ${}^1{Z}_{\text{eff},0}$ is accurately determined to be $0.126\pm 0.002$, which yields an enhancement factor of 1.88 compared with the value 0.067 obtained using the fixed-core stochastic variational method [Phys. Rev. A 65, 034709 (2002)]. Finally, a broad $p$-wave resonance structure is predicted at the incident energy of approximately 0.27 eV, with the annihilation parameter ${}^1{Z}_{\text{eff},1}$ at the resonance center estimated to be around 0.034.

We present a versatile cumulant mapping algorithm for analyzing correlated particle emission, offering insights into complex electronic and nuclear dynamics. Recently, we have demonstrated the use of cumulant mapping to extract information-rich correlations between the momenta of multiple fragments produced in Coulomb explosion imaging experiments [C. Cheng et al., Phys. Rev. Lett. 130, 093001 (2023)]. We define cumulant mapping in terms of histograms, enabling fast computation of linear (additive) observables. However, applying the same algorithm to nonlinear (nonadditive) observables poses challenges, as the computation time of conventional estimators scales nonlinearly with data size. To overcome this, we develop estimators and an accompanying algorithm to enable computationally efficient estimation of the cumulant of interest. Comparisons of computation times and signal-to-noise ratios reveal the superior performance of our approach. This method is demonstrated on the (${\mathrm{D}}^{+}, {\mathrm{D}}^{+}, {\mathrm{C}}^{+}, {\mathrm{O}}^{+}$) dissociation channel of ${\mathrm{CD}}_2{\mathrm{O}}^{4+}$ produced in a strong-field ionization experiment. Additionally, Poisson statistics are used to simulate the two methods and provide insights into the efficiency of our algorithm. The proposed methodology unlocks efficient computation of cumulant mapping for a broader range of complex systems and observables, such as the laser pulse dependence of ionization dynamics.

${\mathrm{N}}_2^{+}$ lasing action involves the creation, evolution, and radiation of ions in intense laser fields. In this paper, we demonstrate that ${\mathrm{N}}_2^{+}$ lasing intensity can be enhanced by several times or totally suppressed by controlling the ionic creation and radiation processes through manipulation of the coherent molecular rotational wave packets of ${\mathrm{N}}_2$ and ${\mathrm{N}}_2^{+}$ with a pump-control scheme. Our results show that if a weak control pulse arrives at the revival moments of the ionic rotational wave packet, the lasing signal can be notably promoted, which is in contrast to observations in previous studies. Meanwhile, the modulation profiles of the lasing signals caused by molecular alignments of ${\mathrm{N}}_2$ and ${\mathrm{N}}_2^{+}$ are analyzed at length, revealing the double roles of the weak control pulse in inducing molecular alignment of ${\mathrm{N}}_2$ or monitoring the amplification of the ${\mathrm{N}}_2^{+}$ system by controlling electronic and rotational coherence. Moreover, by performing a Fourier transformation of the delay-dependent ${\mathrm{N}}_2^{+}$ lasing, the rotational wave-packet information of ${\mathrm{N}}_2$ and ${\mathrm{N}}_2^{+}$ is simultaneously retrieved.

Identifying all-optical high-order harmonic observables as reliable signatures to probe the topology of matter has triggered intense interest. Recently, extensive ab initio simulations challenged the previously explored approaches and proposed a new potential feature, i.e., angular dependence of harmonic yield, as a possible fingerprint of material topology [O. Neufeld et al., Phys. Rev. X 13, 031011 (2023)]. However, nontopological contributions from the band structure, spin-orbit coupling (SOC), and Berry curvature have not been ruled out. Here, we clarify this point by studying the elaborately chosen sample system of monolayer black phosphorus, which exhibits similar band structures and are free from SOC as well as Berry curvature effects for both the trivial and topological phases induced by strain. We find the previously proposed angle-dependent harmonic difference to vanish, suggesting it to be an unreliable observable to probe material topology.

Near two-body unitarity, the three-boson system is characterized by an approximate discrete scale invariance manifest in a geometric tower of bound states (the Efimov effect). In the absence of a strong four-body force, the four-boson system has two states associated with each Efimov state, one very nearly unstable, the other several times deeper. We study correlations between the excited- and ground-state properties, such as binding energies and radii, up to next-to-leading order in an effective field theory for short-range forces. We obtain the parameters in these correlations from similar correlations arising from existing precise calculations based on short-range potentials. We also derive correlations among excited-state properties that emerge from the proximity of the state to the break-up threshold into a boson and a three-boson bound state, using an effective field theory for “halo” states.

We suggest a time-effective single-integral algorithm to calculate tight focusing of a collimated continuous-wave coherent laser beam with an arbitrary cross-section light vector distribution by a high-aperture microscope objective into a planar microcavity. This algorithm is based on the mathematical fact that any beam can be decomposed into a superposition (either finite or infinite) of circularly polarized vortex vector beams, which allows one to factorize the focal field into two parts, one of which depends only on distance coordinates $\rho$ and $z$ and the other one only on an azimuth $\phi$ in cylindrical coordinates. We compare the suggested algorithm with that based on the direct use of the double-integral Richards-Wolf method and demonstrate that the former is from several times to two orders faster for single-point computations and from two to five orders faster for typical focal-region computations. Some existing algorithms based on the discrete Fourier transform can exceed the single-integral algorithm in computational speed up to two orders of magnitude but their accuracy is significantly less and error level is poorly controllable, whereas the single-integral algorithm is able to reproduce field values obtained by the direct Richards-Wolf integration with unlimited accuracy and completely controllable error level.

We study a type-II optical parametric oscillator under injection of laser beams with first-order Hermite-Gauss modes. We develop the equations describing the dynamics of this system in the Wigner representation of the density matrix. These equations are solved numerically and compared with the analytical solution in the nondepletion regime. We show that, when the injected beams are much less intense than the pumping beam, the system still exhibits quantum entanglement, which can be witnessed via Duan-Simon criterion and Bell inequalities. We also propose an experimental apparatus for measuring Bell inequalities. This system can generate spin-orbit hyperentangled states, and is thus a useful resource to quantum technology applications and fundamental physics.

In this paper, the photon blockade effect in a nondegenerate four-wave-mixing system embedded with a two-level atom has been studied. By using an analytical calculation and numerical analysis, we find that both one-photon and two-photon blockade effects could be realized in this system by adjusting the parameters of the system. That is, (i) when the four-wave-mixing interaction and the atom-cavity coupling strength are not equal, the system can realize a one-photon blockade; (ii) when they are consistent with each other, the system can realize a two-photon blockade. In addition, we also discuss the influence of different parameters on the photon blockade effect in detail. The results show that the system constructed in this paper not only could enhance the one-photon blockade effect decisively, but also could implement a two-photon blockade easily with a well-designed energy-level structure, and evidently the blockade effect depends on the parameters of the system. All the results may provide theoretical references for single-photon and multiphoton sources or devices in designing future experiments and practical applications.

Quantum tunneling, as a quintessential quantum phenomenon, has been investigated in detail both theoretically and experimentally. Still, the physical picture of the tunneling process is not intuitive, leading to some confusion and paradoxes. In this paper, we have tried to gain insight into quantum tunneling by a phase-space approach. For this purpose, we scrutinize the evolution of the Wigner distribution during tunneling and derive the energy and momentum spectra by integrating over a segment of phase space. In this way, some of the difficulties and paradoxes in tunneling probability, energy conservation, and tunneling time are given a clearer interpretation. Negative probabilities in the Wigner distribution play a key role in the tunneling process, and the origin of negative probabilities clearly indicates that the volatility of matter underlies the various exotic phenomena involved.