Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave-packet formalism. We demonstrate that whereas the Dirac Hamiltonian impels a causal evolution of probabilities, even in the presence of interactions, the relativistic-Schrödinger model is acausal. We quantify the causality breakdown in the latter model and argue that, in contrast to the popular viewpoint, it is not related to the localization properties of the states.

Nonadiabatic holonomic quantum computation has a robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. To resolve this problem, we here propose a composite scheme to realize nonadiabatic holonomic gates. Our scheme can suppress systematic errors while preserving holonomic robustness. It is particularly useful when the evolution period is shorter than the coherence time. We further show that our composite scheme can be protected by decoherence-free subspaces. In this case, the strengthened robust feature of our composite gates and the coherence stabilization virtue of decoherence-free subspaces are combined.

The orientation of molecules with respect to the laser polarization brings rich physics into laser-molecule interaction. However, the degree of orientation of a polar molecule is difficult to measure in present experiments. Here, through numerical solution of the time-dependent Schrödinger equation, we show that high-order-harmonic generation from polar molecules with a large permanent dipole in ultrashort laser pulses can be used as a sensitive tool to probe the degree of orientation. The underlying mechanism is discussed.

The resonant filtering method transforming the frequency-modulated radiation field into a train of short pulses is proposed to be applied in the optical domain. Effective frequency modulation can be achieved by using an electro-optic modulator. Due to frequency modulation, a narrow-spectrum cw radiation field is seen by the resonant filter as a comb of equidistant spectral components separated by the modulation frequency. Tuning a narrow-bandwidth filter in resonance with the $n\mathrm{th}$ spectral component of the comb transforms the radiation field into bunches of pulses, with $n$ pulses in each bunch. The transformation is explained by the interference of the coherently scattered resonant component of the field with the whole comb. Constructive interference results in the formation of pulses, while destructive interference is seen as dark windows between pulses. It is indicated that the optimal thickness of the resonant filter is several orders of magnitude smaller than the necessary thickness of the dispersive filters used before in the optical domain to produce short pulses from the frequency-modulated field.

We introduce and experimentally implement a method for the detector calibration of photon-number-resolving time-bin multiplexing layouts based on the measured click statistics of superconducting nanowire detectors. In particular, the quantum efficiencies, the dark count rates, and the positive operator-valued measures of these measurement schemes are directly obtained with high accuracy. The method is based on the moments of the click-counting statistics for coherent states with different coherent amplitudes. The strength of our analysis is that we can directly conclude—on a quantitative basis—that the detection strategy under study is well described by a linear response function for the light-matter interaction and that it is sensitive to the polarization of the incident light field. Moreover, our method is further extended to a two-mode detection scenario. Finally, we present possible applications for such well-characterized detectors, such as sensing of atmospheric loss channels and phase sensitive measurements.

We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for the one-dimensional Dirac equation. The properties of the associated intertwining operators are discussed and the explicit form for higher-order transformations is presented. We utilize the results to derive a multiparametric class of exactly solvable systems where the balanced gain and loss represented by the $PT$-symmetric refractive index can imply localization of the electric field in the material.

We study the interplay of spin-orbit coupling (SOC) and strong $p$-wave interactions to the scattering property of spin-$\frac{1}{2}$ ultracold Fermi gases. Based on a two-channel square-well potential generating $p$-wave resonance, we show that the presence of an isotropic SOC, even for its length being much longer than the potential range, can greatly modify the $p$-wave short-range boundary condition (BC). As a result, the conventional $p$-wave BC cannot predict the induced molecules near $p$-wave resonances, which can be fully destroyed due to strong interference between the $s$- and $p$-wave channels. By analyzing the intrinsic reasons for the breakdown of the conventional BC, we propose a $p$-wave BC that can excellently reproduce the exact molecule solutions and also equally apply for a wide class of single-particle potentials besides SOC. This work reveals the significant effect of SOC on both the short- and long-range properties of fermions near $p$-wave resonances, paving the way for future explorations of interesting few- and many-body physics in such systems.

We investigate the role of quantum coherence depletion (QCD) in the Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure (${\mathcal{C}}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure (${\mathcal{C}}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of the database, regardless of using ${\mathcal{C}}_r$ or ${\mathcal{C}}_{l_1}$. In the generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord, and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated.

Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank 2 quantum mixed states: complete analysis for the bipartite states and partial analysis for the multipartite states. For each rank 2 mixed state, we define its unique Bloch sphere, that is spanned by the eigenstates of its density matrix. We characterize those Bloch spheres into exactly five classes of entanglement and separability, give examples for each class, and prove that those are the only classes.

Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is proposed to remove all possible detector side channel attacks without the alignment of reference frames. Due to unavoidable multiphoton events in practical sources, the decoy-state method is always adopted in real-life QKD systems. Unlike original MDI-QKD (O-MDI-QKD), the characterization on practical decoy-state RFI-MDI-QKD is still absent to date. In this paper, we investigate the performance of practical decoy-state RFI-MDI-QKD at different misalignments of reference frames with full parameter optimization when considering statistical fluctuations, and provide a clear comparison between decoy-state RFI-MDI-QKD and O-MDI-QKD. Simulation results demonstrate that decoy-state RFI-MDI-QKD can exhibit performance comparable to that of O-MDI-QKD in practical scenarios, which is very robust in QKD systems.

Laser spectroscopic studies on minute samples of exotic radioactive nuclei require very efficient experimental techniques. In addition, high resolving powers are required to allow extraction of nuclear structure information. Here we demonstrate that by using weak atomic transitions, resonance laser ionization spectroscopy is achieved with the required high efficiency (1%–10%) and precision (linewidths of tens of MHz). We illustrate experimentally and through the use of simulations how the narrow experimental linewidths are achieved and how distorted resonance ionization spectroscopy line shapes can be avoided. The role of the delay of the ionization laser pulse with respect to the excitation laser pulse is crucial: the use of a delayed ionization step permits the best resolving powers and line shapes. A high efficiency is maintained if the intermediate level has a lifetime that is at least of the order of the excitation laser pulse width. A model that describes this process reproduces well the observed features and will help to optimize the conditions for future experiments. The simulation code is available upon request to the authors.

Fully accounting for nondipole effects in the electron dynamics, double ionization is studied for He driven by a near-infrared laser field and for Xe driven by a mid-infrared laser field. Using a three-dimensional semiclassical model, the average sum of the electron momenta along the propagation direction of the laser field is computed. If nondipole effects are not accounted for, the average momentum of each electron in the propagation direction of the laser field is zero. When nondipole effects are accounted for the sum of the electron momenta is found to be an order of magnitude larger than twice the average electron momentum along the propagation direction of the laser field in single ionization. This average sum of the electron momenta is found to be maximum at intensities smaller than the intensities satisfying previously predicted criteria for the onset of magnetic-field effects. It is shown that strong recollisions are the reason for this unexpectedly large value of the sum of the momenta along the direction of the magnetic component of the Lorentz force.

We investigate the Gorkov–Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect exhibits a crossover behavior where the ratio between the estimates without and with the correction first decreases with SOC and then becomes insensitive to SOC when it goes into the strong SOC regime. We demonstrate the applicability of the GM correction by comparing the zero-temperature condensate fraction with the recent quantum Monte Carlo results.

Wave functions will experience a localization process when evolving in disordered lattices. Here, we have demonstrated the effects of disordered $\mathcal{P}\mathcal{T}$-symmetric potentials on wave-function characteristics in optics based on eigenstate analyses. In weak-disorder cases, by using the tight-binding approximation method, a conclusion is obtained that the increasing of the imaginary part of potential can enhance the diffraction, while the increasing disorder will block the diffraction and lead to localization. In the general case, band theory is used for band-structure analysis of three bands. We find that the disorder has a smaller effect on the higher-order band, which is proved by the beam evolutions. Our work may be instructive for realizing beam path control by manipulating the strengths of disorder and gain and/or loss of lattice.

The problem of finding symmetric informationally complete positive-operator-valued-measures (SIC-POVMs) has been solved numerically for all dimensions $d$ up to 67 [A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010)], but a general proof of existence is still lacking. For each dimension, it was shown that it is possible to find a SIC-POVM that is generated from a fiducial state upon application of the operators of the Heisenberg-Weyl group. We draw on the numerically determined fiducial states to study their phase-space features, as displayed by the characteristic function and the Wigner, Bargmann, and Husimi representations, adapted to a Hilbert space of finite dimension. We analyze the phase-space localization of fiducial states, and observe that the SIC-POVM condition is equivalent to a maximal delocalization property. Finally, we explore the consequences in phase space of the conjectured Zauner symmetry. In particular, we construct a Hermitian operator commuting with this symmetry that leads to a representation of fiducial states in terms of eigenfunctions with definite semiclassical features.

In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out that a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two device-independent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to bound the underlying Hilbert space dimension. Second, when the Hilbert space dimension bound is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.

One version of the energy-time uncertainty principle states that the minimum time $T_{\perp }$ for a quantum system to evolve from a given state to any orthogonal state is $h/\left(4\mathrm{\Delta }E\right)$, where $\mathrm{\Delta }E$ is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that $T_{\perp }\ge h/\left(2\langle E\rangle \right)$, where $\langle E\rangle$ is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted $T_{\perp }$ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system's energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to $\langle E\rangle$ and $\mathrm{\Delta }E$ as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

Establishing entanglement between two remote systems by the method of entanglement swapping is an essential step for a long-distance quantum network. Here we report a field-test entanglement swapping experiment with two independent telecommunication band entangled photon-pair sources over an optical fiber network in Hefei. The two sources are located at two nodes that are $12.5\mathrm{km}$ apart and the Bell-state measurement is performed at a third location which is connected to the two source nodes with 14.7-km and 10.6-km optical fibers, respectively. The observed average visibility is $79.9\pm 4.8\%$, which is sufficient for the violation of Bell inequalities. Furthermore, with the swapped entanglement, we demonstrate a source-independent quantum key distribution, which is also immune to any detection attacks at the measurement site.

An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schrödinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall, and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting, respectively, as top and bottom mirrors. We calculate numerically Casimir-Polder shifts of the energies of the cavity resonances and propose an approximate treatment which is precise enough to discuss spectroscopy experiments aimed at tests of the weak-equivalence principle on antihydrogen. We also discuss the lifetimes by calculating complex energies associated with cavity resonances.