Imaginary numbers play an important role in physics, especially in quantum physics. They are not only a part of describing the dynamic behavior of quantum systems, but also play a key role in the phase and interference phenomena of quantum states. Similar to coherence and entanglement, the imaginarity has been regarded as a quantum resource, further revealing the nonclassical properties of quantum systems and providing new research directions and applications for fields such as quantum computing and quantum communication. In our work, we mainly explore the quantitative relationship between imaginarity and entanglement. For an arbitrary quantum state, there exists a general quantitative relationship between imaginarity and entanglement. For a given class of quantum states, where the closest real states to them are diagonal states, there exists an imaginarity-entanglement inequality. We demonstrate that for these quantum states, any degree of imaginarity with respect to some reference basis can be transformed into entanglement through incoherent real operations. This discovery allows us to define an entanglement-based imaginarity quantifier for these states in quantum systems of arbitrary dimensions and to study their properties. It is shown that for these quantum states, imaginarity and entanglement are operationally equivalent. Our work provides a clear quantitative and operational link between imaginarity and entanglement.

Measurement-device-independent entanglement witnesses (MDI-EWs) enable the detection of entanglement without relying on characterized measurements. However, entanglement criteria for MDI-EWs typically assume the idealized condition that the laboratory input states are precisely the desired ones. In this work, we remove this idealization by considering the realistic scenario in which laboratory input states may be imprecise. We specify a class of MDI-EWs, termed sensitive MDI-EWs, whose entanglement criteria fail under any nonzero imprecision in the input states. We derive sufficient conditions for an MDI-EW to be classified as sensitive, revealing that a large class of MDI-EWs exhibit this sensitivity, consistent with the intuition that sensitive MDI-EWs are common. Additionally, we demonstrate that two well-known MDI-EWs for Werner states are sensitive according to our criteria, one of which recovers the result from a previous study [Phys. Rev. A 104, 012429 (2021)]. Moreover, we clarify the concept of laboratory input states in a way that makes imprecisions experimentally measurable and propose a systematic approach for modifying the criterion of any MDI-EW to accommodate small imprecisions, thus enhancing experimental relevance. A simple MDI-EW example is provided, where our modified criterion is already optimal. This work bridges the gap between idealized theoretical models and practical experimental conditions, paving the way for more robust and accessible entanglement detection in real-world settings.

Advanced superresolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to the Cramér-Rao bound (CRB) has proved to be a powerful and efficient tool for resolution analysis and optical setups optimization. However, the standard CRB is not applicable to constrained problems violating the unbiasedness condition, while such models are frequently encountered in quantum imaging of complex objects. Complementary to the existing approaches based on modifying CRB, we propose a practical algorithm for approximate construction of a modified Fisher information matrix, which takes the constraints into account and enables accurate estimation of errors for constrained problems by the standard CRB. We demonstrate the efficiency of the proposed technique by applying it to one-, two-, and multiparameter model problems in quantum imaging. The approach provides quantitative explanation of previous results with successful experimental reconstruction of objects with the spatial scale smaller than the theoretical limit predicted by the standard CRB.

Alkali-metal dimers, ${\mathrm{Ak}}_2$, located on the surface of a helium nanodroplet, are set into rotation through the polarizability interaction with a nonresonant 1-ps-long laser pulse. The time-dependent degree of alignment is recorded using femtosecond-probe-pulse-induced Coulomb explosion into a pair of ${\mathrm{Ak}}^{+}$ fragment ions. The results, obtained for ${\mathrm{Na}}_2$, ${\mathrm{K}}_2$, and ${\mathrm{Rb}}_2$ in both the ground state $1{}^1{\mathrm{\Sigma }}_g^{+}$ and the lowest-lying triplet state $1{}^3{\mathrm{\Sigma }}_u^{+}$, exhibit distinct, periodic revivals with a gradually decreasing amplitude. The dynamics differ from that expected for dimers had they behaved as free rotors. Numerically, we solve the time-dependent rotational Schrödinger equation, including an effective mean-field potential to describe the interaction between the dimer and the droplet. The experimental and simulated alignment dynamics agree well and their comparison enables us to determine the effective rotational constants of the alkali dimers with the exception of ${\mathrm{Rb}}_2$($1{}^3{\mathrm{\Sigma }}_u^{+}$) that only exhibits a prompt alignment peak but no subsequent revivals. For ${\mathrm{Na}}_2$($1{}^3{\mathrm{\Sigma }}_u^{+}$), ${\mathrm{K}}_2$($1{}^1{\mathrm{\Sigma }}_g^{+}$), ${\mathrm{K}}_2$($1{}^3{\mathrm{\Sigma }}_u^{+}$), and ${\mathrm{Rb}}_2$($1{}^1{\mathrm{\Sigma }}_g^{+}$), the alignment dynamics are well described by a two-dimensional rotor model. We ascribe this to a significant confinement of the internuclear axis of these dimers, induced by the orientation-dependent droplet–dimer interaction, to the tangential plane of their residence point on the droplet.

This paper theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For small kick strengths, localized topologically protected bound states exist, and as the kick strengths increase, these states proliferate. However, at large kick strengths they gradually delocalize in stages, eventually becoming random orthonormal vectors as chaos emerges. We identify the delocalization of the bound states as a finite-size effect where their proliferation leads to their eventual overlap. This insight allows us to make analytic predictions for the onset and full emergence of chaos which are supported by numerical results of the quasienergy level spacing ratio and Rényi entropy. A dynamical probe is also proposed to distinguish chaotic from regular behavior.

Haldane's fractional exclusion statistics (FES) describe generalized Pauli exclusion statistics, which can be regarded as emergent quantum statistics induced by the intrinsic dynamical interaction. Nonmutual FES have been identified at the quantum criticality of the one-dimensional (1D) and 2D interacting Bose gas [Nat. Sci. Rev. 9, nwac027 (2022)]. It is naturally asked if such nonmutual FES can be induced by the spin-spin interaction in the antiferromagnetic spin-1/2 $XXX$ chain. In this article, we first represent the Bethe ansatz equations of spin strings in terms of the FES equations of different species. Then we show that the 1D spin $XXX$ chain remarkably possesses nonmutual FES in the critical region. We observe that the equation of state in terms of the FES gives rises to full statistical properties of the model at quantum criticality, which are in good agreement with the results obtained from the thermodynamic Bethe ansatz (TBA) equations of the model. From the nonmutual FES, we also precisely determine the quantum scaling functions, which further agree well with the previous TBA results [Phys. Rev. B 96, 220401(R) (2017)]. Finally, we also establish an exact mapping between the scaling functions of the Lieb-Liniger model and the spin Heisenberg spin chain at quantum criticality. Our method provides deep insights into the critical phase of matter from a quantum FES point of view.

Weyl semimetals are prospective materials to tailor light-matter interaction due to their gyrotropic properties caused by a couple of chiral Weyl points. Here, we study electromagnetic scattering characteristics from infinitely long multilayer cylindrical particles containing Weyl semimetal layers. We develop a modification of operator scattering theory that uses evolution operators to describe a set of layers. We reveal asymmetry in differential scattering cross sections stemming from the axion term of Weyl semimetal permittivity tensor, trace the radiation pattern change for multilayer particles, analyze the interference of lower multipoles with perspective of generalizing the Kerker effect, and carry out multipolar decomposition of the scattered radiation. Both the scattering theory and the numerical results can be useful for device engineering in nanophotonics.

The Tellegen response is a special type of nonreciprocal magnetoelectric coupling which has long remained elusive in photonics and is extremely weak in condensed matter. It is widely accepted that the Tellegen coefficient is restricted by ${\chi }^2<\epsilon \mu$, where $\varepsilon$ and $\mu$ are the permittivity and permeability of the material. Here, we demonstrate that this restriction is lifted in the medium with several close resonances, which provides a theoretical foundation for a giant Tellegen response and enhanced nonreciprocal phenomena.

Hyperbolic metasurfaces exhibit the ability to support surface waves with hyperbolic isofrequency contours (i.e., hyperbolic eigenmodes), offering an exceptional platform for enhancing light-matter interactions. In addition to hyperbolic eigenmodes, hyperbolic metasurfaces can also support the propagation of surface-wave eigenmodes with an antihyperbolic isofrequency contour (i.e., antihyperbolic eigenmodes). In this work, we explore the lesser-known antihyperbolic eigenmodes, highlighting their unique polarization properties compared to hyperbolic eigenmodes. We find that the antihyperbolic eigenmodes at the vertices of the antihyperbolic isofrequency contour and the hyperbolic eigenmodes at the vertices of the hyperbolic isofrequency contour could have purely linear but opposite polarizations. Moreover, we reveal that the manipulation of metasurface's surface conductivity can provide a feasible route to realize the polarization conversion between these linearly polarized antihyperbolic and hyperbolic eigenmodes. That is, the $s$-polarized antihyperbolic eigenmodes would be changed to $p$-polarized ones, while the $p$-polarized hyperbolic eigenmodes are changed to $s$-polarized ones. These findings offer a pathway to selectively excite either hyperbolic or antihyperbolic eigenmodes, enabling control over subwavelength light propagation. Our results provide insights into polarization manipulation and potential applications in nano-optics and photonic devices.

Optical parametric amplifiers (OPAs) in traveling-wave configuration can generate localized spatial quantum correlations between a signal and an idler beam, a useful resource for quantum imaging. To characterize the spatial correspondence between the optical modes of the signal and those of the idler, we look at the classical transverse dynamics of these beams when they propagate in a generic thick OPA at a nominally small angle. In these conditions, the beams tend to copropagate while maintaining a fixed separation, a phenomenon that we term hitching. We develop a model for hitching, validated by a numerical simulation, and provide an experimental demonstration using four-wave mixing in a hot atomic vapor. They show that the OPA gain is the primary influence on the final hitching distance. These results have implications for the generation of multi-spatial-mode squeezed light for quantum imaging applications, where the exact spatial correlations between the quantum fluctuations of the signal and the idler are of prime importance.

A nonlinear optical loop mirror (NOLM) is an optical component commonly used to shape the temporal profile of guided light waves in a large number of optical systems. Although the NOLM is an inherently multifunctional device, in all its practical applications this device is still designed to provide a single functionality. Here we show that the NOLM can be designed to provide multiple functions and make a complex optical system more efficient and competitive. In particular, we show that in a mode-locked laser cavity the NOLM can be designed to serve as a mode-locking element in the transient regime of the laser, and as a power regulator in the stationary regime. While the conventional architecture of a NOLM is usually built from nontunable components, our multifunctional NOLM is built with tunable components offering great flexibility in setting the device's transfer function, and therefore the ability to access different types of optical functions such as pulse regeneration, power regulation, or mode locking in laser cavities.

It is well established that starting only with strong, projective quantum measurements, experiments can be designed to allow weak measurements, which lead to a random walk between the possible final measurement outcomes. However, one can ask the reverse question: starting with only weak measurements, can all the results of standard strong measurements be recovered? Prior work has shown that some results can be, such as the Born rule for the probability of measurement outcomes as a function of wave intensity. In this paper, we show that another crucial result can be reproduced by purely weak measurements, namely, the collapse of a many-body, nonlocally entangled wave function on a timescale comparable to the characteristic time of a single, local measurement. For an entangled state of a single excitation among $N$ qubits, we find the collapse time scales as a double logarithm of $N$. This result affirms the self-consistency of the hypothesis that spontaneous weak measurements lie at the base of all physical measurements, independent of human observers.

Distributed computing, involving multiple servers collaborating on designated computations, faces a critical challenge in optimizing interserver communication—an issue central to the study of communication complexity. Quantum resources offer advantages over classical methods in addressing this challenge. In this work, we investigate a distributed computing scenario with multiple senders and a single receiver, establishing a scalable advantage of multipartite quantum entanglement in mitigating communication complexity. Specifically, we demonstrate that when the receiver and the senders share a multiqubit Greenberger-Horne-Zeilinger (GHZ) state—a quintessential form of genuine multipartite entanglement—certain global functions of the distributed inputs can be computed with only one bit of classical communication from each sender. In contrast, without entanglement, two bits of communication are required from all but one sender. Consequently, quantum entanglement reduces communication overhead by $n-1$ bits for $n$ senders, allowing for arbitrary scaling with an increasing number of senders. We also show that the entanglement-based protocol exhibits significant robustness under white noise, thereby establishing the potential for experimental realization of this quantum advantage.

We present a comprehensive study of the angular distribution of photons emitted during resonant two-photon electron capture by H-like uranium ions. Focusing on the energies of incident electrons, for which the dielectronic recombination (DR) dominates, we analyze the angular emission spectrum of the most significant cascade transitions, which make the main contribution to the total cross section. In particular, we consider the cascade transitions that occur with the formation of $\left(1s2s\right)$ and $\left(1s2p\right)$ intermediate states. We investigate the angular distribution of the emitted photons beyond the single-photon approximation. We separately consider the contributions of the DR and the radiative recombination channels and demonstrate that the two-photon angular distribution shows strong interference between these channels.

We study the collective excitation spectrum of a Raman-induced spin-orbit-coupled spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap while varying either the Raman coupling or quadratic Zeeman field strength by using the Bogoliubov approach. A few low-lying modes, which can be used to delineate the phase boundaries, are identified by exciting them with suitable perturbations. We also investigate the coarsening dynamics of a homogeneous quasi-two-dimensional spin-orbit-coupled spin-1 condensate by quenching from the zero momentum into the plane wave phase through a sudden change in Raman coupling or quadratic Zeeman field strength. We demonstrate that the correlation function of the order parameter displays dynamic scaling during the late-time dynamics, allowing us to determine the dynamic critical exponent.

We introduce a general approximate method for calculating the one-body correlations and the momentum distributions of one-dimensional Bose gases at finite interaction strengths and temperatures trapped in smooth confining potentials. Our method combines asymptotic techniques for the long-distance behavior of the gas (similar to Luttinger liquid theory) with known short-distance expansions. We derive analytical results for the limiting cases of strong and weak interactions and provide a general procedure for calculating one-body correlations at any interaction strength. A step-by-step explanation of the numerical method used to compute Green's functions (needed as input to our theory) is included. We benchmark our method against exact numerical calculations and compare its predictions to recent experimental results.

Mode coupling has been proven to be an effective method for initiating modulational instability (MI) in a normal-dispersion microresonator. In various mode-coupling systems, mode loss perturbation occurs alongside mode frequency perturbation. In this study, we present a detailed analysis of MI induced by either loss or frequency perturbations added to the pump mode of a normal-dispersion cavity. By distinguishing the individual contributions of frequency and loss perturbations to MI gain, we demonstrate that, in addition to the widely studied frequency perturbation, the introduction of an additional loss to the pump mode can also induce MI even without frequency perturbation, enabling the spontaneous excitation of frequency combs. The effects of pump mode perturbations in various mode-coupling schemes are compared, revealing that loss perturbation has a more significant impact when the pump power is relatively low or when the auxiliary mode experiences a sufficiently higher loss than the main mode. Our findings provide an alternative perspective on illustrating the underlying mechanisms of normal-dispersion Kerr frequency combs generation aided by mode perturbation.

This work introduces a graph-phased Szegedy's quantum walk, which incorporates link phases and local arbitrary phase rotations (APR), unlocking new possibilities for quantum algorithm efficiency. We demonstrate how to adapt quantum circuits to these advancements, allowing phase patterns that ensure computational practicality. The graph-phased model broadens the known equivalence between coined quantum walks and Szegedy's model, accommodating a wider array of coin operators. Through illustrative examples, we reveal intriguing disparities between classical and quantum interpretations of walk dynamics. Remarkably, local APR phases emerge as powerful tools for marking graph nodes, optimizing quantum searches without altering graph structure. We further explore the surprising nuances between single and double operator approaches, highlighting a greater range of compatible coins with the latter. To facilitate these advancements, we present an improved classical simulation algorithm, which operates with superior efficiency. This study not only refines quantum walk methodologies but also paves the way for future explorations, including potential applications in quantum search and PageRank algorithms. Our findings illuminate the path towards more versatile and powerful quantum computing paradigms.

In this paper we introduce the concept of stabilizer convolution and demonstrate that the only convolutions that can be used for stability testing are stabilizer convolutions. Moreover, using any stabilizer convolution yields similarly good results. Through the Choi-Jamiołkowski isomorphism, this method can also be applied to Clifford testing for quantum gates. Leveraging the invariance of circuit magic classes of mean states under stabilizer self-convolution, we formulate a central limit theorem for circuit magic classes of quantum states. Moreover, employing the Choi-Jamiołkowski correspondence, we generalize this finding to establish a central limit theorem for circuit magic classes of completely positive and trace-preserving channels.