Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a deviation from its exact form may lead to a violation of the second law of thermodynamics. Are there deep and natural principles which uniquely determine its form? Here we work within a general epistemic framework for a class of nonclassical theories, introducing an epistemic restriction to an otherwise classical theory, so that the distributions of positions are irreducibly parametrized by the underlying momentum fields. It was recently shown that the mathematics of quantum mechanics formally arises within an operational scheme, wherein an agent makes a specific estimation of the momentum given information on the positions and the experimental settings. Moreover, quantum uncertainty can be traced back to the “specific” choice of estimator and the associated estimation error. In the present work, we show that a plausible inferential-causality principle of estimation independence, which requires that the estimation of momentum of one system must be independent of the position of another system independently prepared of the first, singles out the specific forms of the estimator, and especially the estimation error up to its strength given by a global-nonseparable random variable on the order of Planck constant.

In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of permissible error combinations. By defining the weighted $f$-mean of estimation error and quantum Fisher information, we derive various quantum Cramér-Rao bounds on mean error in a very general form and give their refined versions with complex quantum Fisher information matrices. We show that the geometric- and harmonic-mean quantum Cramér-Rao bounds can help to reveal a larger forbidden region of estimation error for a complex signal in coherent light accompanied by a thermal background than just using the ordinary arithmetic-mean version. Moreover, we show that the $f$-mean quantum Fisher information can be considered as information-theoretic quantities and is useful in quantifying asymmetry and coherence as quantum resources.

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multiqudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

We theoretically investigate the dynamic processes of solid harmonics generation using the one-dimensional time-dependent density functional theory and the three-band recollision model. Compared with gas harmonics, more quantum paths contribute to the generation of solid harmonics. Moreover, the number of quantum paths further increases as the laser vector potential increases. Analysis indicates that the multiple velocity reversals of electrons play an important role in the generation of solid harmonics, which induces multiple collisions of electrons and holes and forms more quantum paths. Besides, we find that the dephasing effect cannot reduce the number of quantum paths. Finally, the relationship between harmonic order and the electron migration distance is also studied. It is found that there is no unified dependence between harmonic order and the electron migration distance because this relationship is path dependent. Our work can contribute to a considerable understanding of the recollision dynamics of solid harmonic generation, which provides the possibility of manipulating the generation of solid harmonics in the future.

Optical potentials have been a versatile tool for the study of atomic motions and many-body interactions in cold atoms. Recently, optical subwavelength single barriers were proposed to enhance the atomic interaction energy scale, which is based on nonadiabatic corrections to Born-Oppenheimer potentials. Here we present a study for creating an alternative landscape of nonadiabatic potentials—multiple barriers with subwavelength spacing at tens of nanometers. To realize these potentials, spatially rapid-varying dark states of atomic $\mathrm{\Lambda }$ configurations are formed by controlling the spatial intensities of the driving lasers. As an application, we show that bound states of very long lifetimes on the order of seconds can be realized. Imperfections and experimental realizations of the multiple barriers are also discussed.

We study by quantum Monte Carlo simulations the low-temperature phase diagram of dipolar bosons confined to one dimension, with dipole moments aligned along the direction of particle motion. A hard-core repulsive potential of varying range ($\sigma$) is added to the dipolar interaction, in order to ensure stability of the system against collapse. In the $\sigma \to 0$ limit the physics of the system is dominated by the potential energy and the ground state is quasicrystalline; as $\sigma$ is increased the attractive part of the interaction weakens and the equilibrium phase evolves from quasicrystalline to a nonsuperfluid liquid. At a critical value ${\sigma }_c$, the kinetic energy becomes dominant and the system undergoes a quantum phase transition from a self-bound liquid to a gas. In the gaseous phase with $\sigma \to {\sigma }_c$, at low density attractive interactions bring the system into a “weak” superfluid regime. However, gas-liquid coexistence also occurs, as a result of which the topologically protected superfluid regime is not approached.

Generation and manipulation of many-body entangled states is of considerable interest, for applications in quantum simulation or sensing, for example. Measurement and verification of the resulting many-body state presents a formidable challenge, however, which can be simplified by multiplexed readout using shared measurement resources. In this work, we analyze and demonstrate state retrodiction for a system of optomechanical oscillators coupled to a single-mode optical cavity. Coupling to the shared cavity field facilitates simultaneous optical measurement of the oscillators' transient dynamics at distinct frequencies. Optimal estimators for the oscillators' initial state can be defined as a set of linear matched filters, derived from a detailed model for the detected homodyne signal. We find that the optimal state estimate for optomechanical retrodiction is obtained from high-cooperativity measurements, reaching estimate sensitivity at the standard quantum limit (SQL). Simultaneous estimation of the state of multiple oscillators places additional limits on the estimate precision, due to the diffusive noise each oscillator adds to the optomechanical signal. However, we show that the sensitivity of simultaneous multimode state retrodiction reaches the SQL for sufficiently well-resolved oscillators. Finally, an experimental demonstration of two-mode retrodiction is presented, which requires further accounting for technical fluctuations of the oscillator frequency.

Quantum control of photons has become an area of great interest in the development of quantum technology. Here we explore how an external magnetic field can be exploited to control the statistical properties of photons in a bimodal cavity quantum electrodynamics (CQED) system. Our CQED system is composed of a bimodal micropillar Fabry-Pérot cavity containing a single $V$-level quantum dot (QD) involving fine-structure-splitting neutral exciton transitions under the effect of the applied magnetic field in the presence of an incident pump laser field driving one cavity mode. With the introduction of the external magnetic field, not only is the conversion of polarization characteristics of photons achieved, but the statistics properties of photons are well engineered and the switching between photon bunching and antibunching is realized in the weak-coupling regime of CQED. The superiority of our system is manifested in the following aspects. (i) Using experimental parameters, we can manipulate the statistical properties of photons by appropriately tuning the strength of the magnetic field under the weak-coupling CQED condition, accompanied by either enhanced antibunching or a transition from antibunching to strong bunching of the light and vice versa. So we can arrive at selective photon statistics. (ii) The strong photon antibunching effect, under nonresonant scenarios but without the need to match the resonant or near-resonant conditions for the cavity and QD, can appear. Furthermore, we find that the multifrequency photon blockade can be generated in the present system, which is different from previous studies about photon blockade only for specific optical detuning. (iii) The high photon occupations or transmissions, simultaneously accompanied by strong photon antibunching in the system, are beneficial to the correlation measurement in practical experiments. This process works with a high quality of photon antibunching and bunching over a wide range of parameters and has potential applications in on-chip quantum information processing. It is hoped that the proposed scheme provides a possibility for the generation of tunable single-photon sources or controllable photon quantum gates.

We investigate the linear and nonlinear optical response to an optical pumping of a four-level atomic system with electromagnetically induced transparency (EIT) in a cold Rydberg atomic gas. It is found that the transient behavior (especially, the third- and fifth-order susceptibilities) of the probe field, and the steady-state EIT spectrum of the gas, depend crucially on the Rydberg atoms’ interaction. Furthermore, we find that the response speed of the Rydberg interaction with EIT can be as much as six times faster than the EIT without the Rydberg interaction, and that the nonlinear response time of the fifth-order optical susceptibility is longer than that of the third-order susceptibility. It is established that the Rydberg blockade effect plays a significant role in increasing the response speed of the Rydberg with EIT.

X-ray transient absorption spectra (XTAS) of molecules are theoretically investigated in a femtosecond x-ray pump and continuous-wave (cw) infrared (IR)-control scenario. The scheme is exemplified by a CO molecule resonantly pumped into carbon and oxygen core-excited $1\mathrm{s}\to {\pi }^{*}$ states by a weak femtosecond x-ray pulse, while dynamic Stark shifts are induced by the cw IR-control radiation. As a result, significant shoulder structures appear in XTAS showing strong dependence on the phase of IR radiation relative to the envelope of the x-ray pulse. Due to a significant difference in the frequencies of the two pulses, the present XTAS scheme provides much clear interpretation of the dynamic Stark effects as compared to the attosecond UV transient absorption scenario. Within the suggested two-level model, where the total spectrum is decomposed as incoherent superposition of contributions from different vibrational excitations weighted by the Franck-Condon Factors, all spectral structures can be well identified and interpreted in a good agreement with the full-scale molecular simulations. Well-characterized XTAS in the proposed IR-control scheme can be applied for fine phase synchronization between IR and x-ray pulses, highly demanded in modern experiments on x-ray free-electron lasers.

We present an efficient method to compute short-time expectation values in large collective spin systems with typical forms of Markovian decoherence. Our method is based on a Taylor expansion of a formal solution to the equations of motion for Heisenberg operators. This expansion can be truncated at finite order to obtain virtually exact results at short times that are relevant for metrological applications such as spin squeezing. In order to evaluate the expansion for Heisenberg operators, we compute the relevant structure constants of a collective spin operator algebra. We demonstrate the utility of our method by computing spin squeezing, two-time correlation functions, and out-of-time-ordered correlators for ${10}^4$ spins in strong-decoherence regimes that are otherwise inaccessible via existing numerical methods. Our method can be straightforwardly generalized to the case of a collective spin coupled to bosonic modes, relevant for trapped ion and cavity QED experiments, and may be used to investigate short-time signatures of quantum chaos and information scrambling.

We study the existence and characterization of self-trapping phenomena in discrete-time quantum walks. By considering a Kerr-like nonlinearity, we associate an acquisition of the intensity-dependent phase with the walker while it propagates on the lattice. Adjusting the nonlinear parameter $\chi$ and the quantum gates $\theta$, we will show the existence of different quantum walking regimes, including those with traveling solitonlike structures or localized by self-trapping. The latter scenario is absent for quantum gates close enough to the Pauli-$X$ gate. It appears for intermediate configurations and becomes predominant as quantum gates get closer to the Pauli-$Z$ gate. By using $\chi$ versus $\theta$ diagrams, we will show that the threshold between quantum walks with delocalized or localized regimes exhibits an unusual aspect in which an increment of the nonlinear strength can induce the system to transition from a localized to a delocalized regime.

Using a fully stochastic numerical scheme, we theoretically investigate the behavior of a nanolaser in the lasing transition region under the influence of intensity feedback. Studying the input-output curves as well as the second-order correlations for different feedback fractions, we obtain an insight into the role played by the fraction of photons reinjected into the cavity. Our results reveal that the transition shrinks and moves to lower pump values with the feedback strength, and irregular pulses can be generated when the feedback is sufficiently large. The interpretation of the observation is strengthened through the comparison with the temporal traces of the emitted photons and with the radio-frequency power spectra. These results provide insight into the physics of nanolasers as well as validating the use of the second-order autocorrelation as a sufficient tool for interpretation of the dynamics. This confirmation offers a solid basis for the reliance on autocorrelations in experiments studying the effects of feedback in nanodevices.

Having a broad range of methods available for implementing unitary operations is crucial for quantum information tasks. We study a dissipative process commonly used to describe dissipatively coupled systems and show that the process can lead to pure unitary dynamics on one part of a bipartite system, provided that the process is strong enough. As a consequence of these findings, we discuss within the framework of quantum control theory how the dissipative process can enable universal control of the considered part, thereby turning parts of the system into a system capable of universal quantum information tasks. We characterize the time scales necessary to implement gates with high fidelity through the dissipative evolution. The considered dissipative evolution is of particular importance since it can be engineered in the laboratory in the realm of superconducting circuits. Based on a reservoir that is formed by a lossy microwave mode we present a detailed study of how our theoretical findings can be realized in an experimental setting.

We propose a continuous-variable quantum secret sharing (CV-QSS) protocol in which the quantum states are prepared passively using a thermal source. In our protocol, one player splits the output of a thermal source into two spatial modes with the help of a beam splitter, then he (or she) measures one of the correlated thermal states and sends the others to the secure station of the adjacent player in sequence after using appropriate optical attenuation, which waives the necessity of employment of high extinction ratio modulators with good stability. Therefore, the proposed protocol provides convenient implementation in QSS framework. Moreover, our scheme is immune to Trojan horse attacks. We derive the security bounds for our protocol against both eavesdroppers and dishonest players. Furthermore, we can achieve tighter bound of QSS distance by considering the finite-size effect, which is more practical than that obtained in the asymptotic limit.

It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a bipartite finite-dimensional Hilbert space. These methods amount to joint Schmidt-type decompositions of two pure states where the two sets of coefficients and local bases depend on the properties of either state, however, at the expense of the local bases not all being orthonormal and in one case the complex-valuedness of the coefficients. With these results we derive several generally valid purity-type formulas for one-party reductions of rank-1 operators, and we point out relevant relations between the Schmidt decomposition and the Bloch representation of bipartite pure states.

The inner-shell electron-impact excitation from the ground state to the $1s2s^{2}2p_{1/2}{J}_f=1$ excited state and the subsequent electric-dipole $1s2s^{2}2p_{1/2}{J}_f=1\to 1s^{2}2s^2{J}_i=0$ radiative decay of berylliumlike ions with zero nuclear spin have been studied within the framework of the multiconfigurational Dirac-Fock method and the relativistic distorted-wave theory. Special attention has been paid to answering the question of how the Breit interaction affects such a two-step “excitation plus decay” process. To this end, we explore the effect of the Breit interaction on the second-order alignment parameter of the excited state and also the angular distribution of the emitted characteristic photons. It is found that, for low-$Z$ berylliumlike ions such as ${\mathrm{Ne}}^{6+}$, the Breit interaction hardly contributes to the alignment and the angular distribution even at high-impact electron energies. In contrast, the contribution from the Breit interaction for intermediate- and high-$Z$ ions such as ${\mathrm{Mo}}^{38+}, {\mathrm{W}}^{70+}$, and ${\mathrm{U}}^{88+}$ is of the essence, and such a contribution becomes more and more significant with increasing atomic number and electron energy. To be more specific, the Breit interaction even changes qualitatively the relative population of the magnetic substates of the excited state as described by the alignment parameter and the angular emission pattern of the characteristic photons, for example, for ${\mathrm{W}}^{70+}$ and ${\mathrm{U}}^{88+}$ ions at the electron energies beyond 3.5 and 3.3 times the excitation thresholds, respectively.

A model-potential method is employed to calculate binding, elastic scattering, and annihilation of positrons for a number of atoms and small nonpolar molecules, namely, Be, Mg, He, Ar, ${\mathrm{H}}_2, {\mathrm{N}}_2, {\mathrm{Cl}}_2$, and ${\mathrm{CH}}_4$. The model potential contains one free parameter for each type of atom within the target. Its values are chosen to reproduce existing ab initio positron-atom binding energies or scattering phase shifts. The calculations are performed using a Gaussian basis for the positron states, and we show how to obtain values of the scattering phase shifts and normalized annihilation rate $Z_{\text{eff}}$ from discrete positive-energy pseudostates. Good agreement between the present results and existing calculations and experimental data, where available, is obtained, including the $Z_{\text{eff}}$ value for ${\mathrm{CH}}_4$, which is strongly enhanced by a low-lying virtual positron state. An exception is the room-temperature value of $Z_{\text{eff}}$ for ${\mathrm{Cl}}_2$, for which the present value is much smaller than the experimental value obtained over 50 years ago. Our calculations predict that among the molecular targets studied, only ${\mathrm{Cl}}_2$ might support a bound state for the positron, with a binding energy of a few meV.

Microcavity electron-hole-photon systems in two dimensions have long been anticipated to exhibit a crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid when the carrier density is tuned to reach the Mott transition density. Yet, a theoretical understanding of such a BEC-BCS crossover largely relies on the mean-field framework and the nature of the carriers at the crossover remains unclear to some extent. Here, motivated by the recent demonstration of a BCS polariton laser [arXiv:1902.00142] and based on a simplified short-range description of the electron-hole attraction, we examine the role of quantum fluctuations in an exciton-polariton condensate at thermal equilibrium and determine the number of different types of carriers at the crossover beyond mean field. Near Mott density and with very strong light-matter coupling, we find an unexpectedly large phase window for a strongly correlated BCS polariton condensate, where both fermionic Bogoliubov quasiparticles and bosonic excitons are significantly populated and strongly couple to photons. We predict its absorption spectrum and show that the upper polariton energy gets notably renormalized, giving rise to a high-energy side-peak at large carrier density, as observed in recent experiments.