Quantum frequency estimation under general noise is investigated in the Bayesian parameter estimation approach. To evaluate the accuracy of estimation, the Bayes cost is obtained analytically which can be applied to the common noisy channels, such as the phase-damping channel, the amplitude-damping channel, and the depolarizing channel. The Bayes cost formula clearly shows that the prior information imposes a restriction upon the effect of noise in the estimation process. Three examples of frequency estimations are provided to illustrate the roles of prior probability in the estimation process. It is found that, due to the restriction of prior information on the noise, the estimation accuracy is less sensitive to the noise in the Bayesian approach than that in the Cramér-Rao bound approach. More prior information can help us to use the non-Gaussianity of the noise channel to improve the estimation accuracy in the phase-damping channel.

Previous experimental tests of quantum contextuality based on the Bell-Kochen-Specker (BKS) theorem have demonstrated that not all observables among a given set can be assigned noncontextual eigenvalue predictions, but have never identified which specific observables must fail such assignment. We now remedy this shortcoming by showing that BKS contextuality can be confined to particular observables by pre- and postselection, resulting in anomalous weak values that we measure using modern neutron interferometry. We construct a confined contextuality witness from weak values, which we measure experimentally to obtain a $5\sigma$ average violation of the noncontextual bound, with one contributing term violating an independent bound by more than $99\sigma$. This weakly measured confined BKS contextuality also confirms the quantum pigeonhole effect, wherein eigenvalue assignments to contextual observables apparently violate the classical pigeonhole principle.

Microwave photons have become very important qubits in quantum communication, as the first quantum satellite has been launched successfully. Therefore, it is a necessary and meaningful task for ensuring the high security and efficiency of microwave-based quantum communication in practice. Here, we present an original polarization entanglement purification protocol for nonlocal microwave photons based on the cross-Kerr effect in circuit quantum electrodynamics (QED). Our protocol can solve the problem that the purity of maximally entangled states used for constructing quantum channels will decrease due to decoherence from environment noise. This task is accomplished by means of the polarization parity-check quantum nondemolition (QND) detector, the bit-flipping operation, and the linear microwave elements. The QND detector is composed of several cross-Kerr effect systems which can be realized by coupling two superconducting transmission line resonators to a superconducting molecule with the $N$-type level structure. We give the applicable experimental parameters of QND measurement system in circuit QED and analyze the fidelities. Our protocol has good applications in long-distance quantum communication assisted by microwave photons in the future, such as satellite quantum communication.

Greenberger-Horne-Zeilinger (GHZ) and cluster states are two typical kinds of multipartite entangled states and can respectively be used for realizing quantum networks and one-way computation. We propose a feasible scheme for generating Gaussian GHZ and cluster states of multiple mechanical oscillators by pulsed cavity optomechanics. In our scheme, each optomechanical cavity is driven by a blue-detuned pulse to establish quantum steerable correlations between the cavity output field and the mechanical oscillator, and the cavity outputs are combined at a beam-splitter array with given transmissivity and reflectivity for each beam splitter. We show that by harnessing the light-mechanical steerable correlations, the mechanical GHZ and cluster states can be realized via homodyne detection on the amplitude and phase quadratures of the output fields from the beam-splitter array. These achieved mechanical entangled states can be viewed as the output states of an effective mechanical beam-splitter array with the mechanical inputs prepared in squeezed states with the light-mechanical steering. The effects of detection efficiency and thermal noise on the achieved mechanical states are investigated. The present scheme does not require externally injected squeezing and it can also be applicable to other systems such as light-atomic-ensemble interface, apart from optomechanical systems.

We show that any Bell local state with a hidden nonlocality that can be revealed by local filtering is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states can be revealed by local operations and the sending of two one-bit messages, one in each direction. For some particular states, one bit of communication is even enough.

A ($k,n$)-threshold secret-sharing scheme allows for a string to be split into $n$ shares in such a way that any subset of at least $k$ shares suffices to recover the secret string, but such that any subset of at most $k-1$ shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a ($n,n$)-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an $n$-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an $n$-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

We propose a counterfactual $1\to 2$ economical phase-covariant cloning scheme. Compared with the existing protocols using flying qubits, the main difference of the presented scheme is that the cloning can be achieved without transmitting the photon between the two parties. In addition, this counterfactual scheme does not need to construct controlled quantum gates to perform joint logical operations between the cloned qubit and the blank copy. We also numerically evaluate the performance of the present scheme in the practical experiment, which shows this cloning scheme can be implemented with a high success of probability and the fidelity is close to the optimal value in the ideal asymptotic limit.

We show that the distillable coherence—which is equal to the relative entropy of coherence—is, up to a constant factor, always bounded by the ${\ell }_1$-norm measure of coherence (defined as the sum of absolute values of off diagonals). Thus the latter plays a similar role as logarithmic negativity plays in entanglement theory and this is the best operational interpretation from a resource-theoretic viewpoint. Consequently the two measures are intimately connected to another operational measure, the robustness of coherence. We find also relationships between these measures, which are tight for general states, and the tightest possible for pure and qubit states. For a given robustness, we construct a state having minimum distillable coherence.

The complex Kohn variational method for electron–polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential ${\widehat{G}}_0^{+}\widehat{V}$ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the $T$ matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and ${\mathrm{CF}}_4$ in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Double-differential cross section (DDCS) for electrons ejected in collisions of fast ${\mathrm{C}}^{6+}$ and ${\mathrm{Si}}^{13+}$ projectiles, with a ${\mathrm{H}}_2\mathrm{O}$ vapor target, were measured. The electrons were detected over an energy range of 1–600 eV and an angular range of ${20}^{\circ }$–${160}^{\circ }$. The obtained DDCS spectra, for both the ions, were compared with the CDW-EIS model. Occasional reference has been made to the DDCS data for the case of 3.75-MeV/u ${\mathrm{O}}^{8+}$ colliding on the same molecule for an overall comparison. A reasonable agreement with theoretical results was seen for the case of ${\mathrm{C}}^{6+}$ and ${\mathrm{O}}^{8+}$ projectiles. However, between ${\mathrm{C}}^{6+}$ and ${\mathrm{O}}^{8+}$ projectiles, the deviation from theory is larger for the case of the carbon projectile. Substantial deviation starts to show up for the case of the ${\mathrm{Si}}^{13+}$ projectile. By numerical integration of the DDCS data, the single-differential cross section (SDCS) and total cross section (TCS) were obtained and compared with theoretical models. The present TCS data along with the other available data for $p$, $\mathrm{He}$, and $\mathrm{C}$ ions were plotted together. A clear and gradual deviation from the Bethe-Born predicted $q^2$ scaling was observed, where $q$ is the projectile charge state. From all the data we find TCS varies as $q^n$ where $n$ = 1.7 $\pm$ 0.1. The provided data set will be valuable in order to help model the radiation damage in hadron therapy, particularly in the Bragg peak region.

By numerically solving the time-dependent Schrödinger equation for helium in its full dimensionality, we determine the joint momentum spectrum along the polarization direction $P(k_{1z},k_{2z})$ for two-photon double ionization (TPDI). We identify features uniquely attributable to dynamical correlation effects in the double continuum. We show that some of the correlation signatures persist in integrated measures, in particular the emission asymmetry, that should become accessible with upcoming XUV light sources. We also compare with predictions of analytic models for TPDI which neglect such final-state correlations.

One-dimensional Bose gases are a useful testing ground for quantum dynamics in many-body theory. They allow experimental tests of many-body theory predictions in an exponentially complex quantum system. Here we calculate the dynamics of a higher-order soliton in the mesoscopic case of $N={10}^3$–${10}^4$ particles, giving predictions for quantum soliton breather relaxation. These quantum predictions use a truncated Wigner approximation, which is a $1/N$ expansion, in a regime where other exactly known predictions are recovered to high accuracy. Such dynamical calculations are testable in forthcoming Bose-Einstein-condensate experiments.

We study theoretically and experimentally the behavior of a strongly confined dipolar Bose-Einstein condensate in the regime of quantum-mechanical stabilization by beyond-mean-field effects. Theoretically, we demonstrate that self-organized “striped” ground states are predicted in the framework of the extended Gross-Pitaevskii theory. Experimentally, by tilting the magnetic dipoles we show that self-organized striped states can be generated, likely in their metastable state. Matter-wave interference experiments with multiple stripes show that there is no long-range off-diagonal order (global phase coherence). We outline a parameter range where global phase coherence could be established, thus paving the way towards the observation of supersolid states in this system.

High-order harmonic spectra from solid materials driven by single-color multicycle laser fields sometimes contain even harmonics. In this work we attribute the appearance of even harmonics to the nonzero transition dipole phase (TDP) when the solid system has broken symmetry. By calculating the harmonic efficiency from graphene and gapped graphene by using the semiconductor Bloch equations under the tight-binding approximation, we demonstrate the role of the TDP, which has been ignored for a long time. When the crystal has inversion symmetry, or reflection symmetry with the symmetry plane perpendicular to the laser polarization direction, the TDP can be neglected. Without such symmetry, however, the TDP will lead to the appearance of even harmonics. We further show that the TDP is sensitive to the crystal geometry. To extract the structure information from the harmonic spectra of a solid the TDP cannot be ignored.

Macroscopic quantum superposition states are fundamental to test the classical-quantum boundary and present suitable candidates for quantum technologies. Although the preparation of such states has already been realized, the existing setups commonly consider external driving and resonant interactions, predominantly by considering Jaynes-Cummings-like and beam-splitter-like interactions, as well as the nonlinear radiation pressure interaction in cavity optomechanics. In contrast to previous works on the matter, we propose a feasible probabilistic scheme to generate a macroscopic mechanical qubit, as well as phononic Schrödinger's cat states with no need of any energy exchange with the macroscopic mechanical oscillator. Essentially, we investigate an open dispersive spin-mechanical system in the absence of any external driving under nonideal conditions, such as the detrimental effects due to the oscillator and spin energy losses in a thermal bath at nonzero temperature. In our work, we show that the procedure to generate the mechanical qubit state is solely based on spin postselection in the weak to moderate coupling regime. Finally, we demonstrate that the mechanical superposition is related to the amplification of the mean values of the mechanical quadratures as they maximize the quantum coherence.

In front of a mirror, the radiation of weakly driven large disordered clouds presents an interference fringe in the backward direction, on top of an incoherent background. Although strongly driven atoms usually present little coherent scattering, we show here that the mirror-assisted version can produce high contrast fringes, for arbitrarily high saturation parameters. The contrast of the fringes oscillates with the Rabi frequency of the atomic transition and the distance between the mirror and the atoms, due to the coherent interference between the carrier and the Mollow sidebands of the saturated resonant fluorescence spectrum emitted by the atoms. The setup thus represents a powerful platform to study the spectral properties of ensembles of correlated scatterers.

We propose to construct a nonreciprocal single-photon frequency converter via multiple semi-infinite coupled-resonator waveguides (CRWs). We first demonstrate that the frequency of a single photon can be converted nonreciprocally through two CRWs, which are coupled indirectly by optomechanical interactions with two nondegenerate mechanical modes. Based on this nonreciprocity, two different single-photon circulators are proposed in the $\mathsf{T}$-shaped waveguides consisting of three semi-infinite CRWs, which are coupled pairwise by optomechanical interactions. One circulator is proposed by using two nondegenerate mechanical modes and the other one is proposed by using three nondegenerate mechanical modes. Nonreciprocal single-photon frequency conversion is induced by breaking the time-reversal symmetry, and the optimal conditions for nonreciprocal frequency conversion are obtained. These proposals can be used to realize nonreciprocal frequency conversion of single photons in any two distinctive waveguides with different frequencies and they can allow for dynamic control of the direction of frequency conversion by tuning the phases of external driving lasers, which may have versatile applications in hybrid quantum networks.

We investigate Beliaev-Landau scattering in a gas of interacting photons in a coherently driven array of nonlinear dissipative resonators, as described by the one-dimensional driven-dissipative Bose-Hubbard model. Due to the absence of detailed balance in such an out-of-equilibrium setup, steady-state properties can be much more sensitive to the underlying microscopic dynamics. Because the popular truncated Wigner approximation dramatically fails in capturing this physics, we present an alternative approach, based on a systematic expansion beyond the Bogoliubov approximation, which includes the third-order correlation functions in the dynamics. As experimentally accessible signatures of Beliaev-Landau processes, we report a small but non-negligible correction to the Bogoliubov prediction for the steady-state momentum distribution, in the form of a characteristic series of peaks and dips, as well as non-Gaussian features in the statistics of the cavity output field.