We show an experimental procedure to certify the classical capacity for noisy qubit channels. The method makes use of a fixed bipartite entangled state, where the system qubit is sent to the channel input and the set of local measurements, ${\sigma }_x\otimes {\sigma }_x, {\sigma }_y\otimes {\sigma }_y$, and ${\sigma }_z\otimes {\sigma }_z$, is performed at the channel output and the ancilla qubit, thus without resorting to full quantum process tomography. The witness to the classical capacity is then achieved by reconstructing sets of conditional probabilities, noise deconvolution, and classical optimization of the pertaining mutual information. The performance of the method to provide lower bounds to the classical capacity is tested by a two-photon polarization entangled state in Pauli channels and amplitude damping channels. The measured lower bounds to the channels are in high agreement with the simulated data, which take into account both the experimental entanglement fidelity $F=0.979\pm 0.011$ of the input state and the systematic experimental imperfections.

We first investigate the one-shot static entanglement cost to simulate a bipartite quantum channel under the set of nonentangling channels. The lower bound on the one-shot static entanglement cost is given by the generalized robustness of the target channel as well as the robust-generating power of the channel, which implies that the cost necessary to generate a bipartite quantum channel might not be retrievable in general. Next, we conceive a set of quantum channels that extends the set of nonentangling channels. We find out that the one-shot static entanglement cost under the extended set of channels is given by the channel's standard log-robustness. This quantity also gives the one-shot dynamic entanglement cost under a set of free superchannels that do not generate a dynamic entanglement resource; the extended set is shown to be equivalent to the set of free superchannels.

Multiple-qubit quantum logic gates are an important element in the implementation of quantum computers. The direct construction of multiple-qubit quantum logic gates in an efficient way has important values compared to the construction of multiple-qubit gates using a series of two-qubit and single-qubit gates. We propose a scheme to construct a multiple-qubit ${\mathrm{C}}_k\mathrm{U}$ gate ($k$ denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.

A linear relation is found between Jaynes entropy and the correlation energy associated with the cumulant for a correlated molecular system, as demonstrated in ${\mathrm{H}}_2$ and a water molecule. The relation modifies the Collins conjecture, in which the correlation energy is defined as the total energy difference with reference to the Hartree-Fock counterpart. The linear behavior is system dependent and shifts slightly on a different basis set. This correlation energy is extensive. For a system whose wave function can be expressed as the antisymmetrized product of orthogonal groups, the correlation energy is just the sum of the individual groups. The finding offers a convenient way to construct an approximate correlation energy functional in reduced density-matrix-functional theory, which may be used in large-scale molecular dynamics simulations and potential energy surface calculations where the molecular geometry needs to be frequently updated.

Experiments have demonstrated that the excitation of atoms embedded in a Bose-Einstein condensate to Rydberg states is accompanied by phonon creation. Here we provide the theoretical basis for the description of phonon-induced decoherence of the superposition of two different Rydberg states. To this end, we determine Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities, and reorganization energies. These quantities characterize the influence of the environment and form essential inputs for followup open quantum system approaches. We find that the amplitude of bath correlations scales like the power law ${\nu }^{-6}$ with the principal quantum number $\nu$, while reorganization energies scale exponentially, reflecting the extreme tunability of Rydberg atomic properties.

Spatially engineered photons from spontaneous parametric down-conversion (SPDC) are a valuable tool for studying and applying photonic entanglement. An advantage of SPDC is that simple expressions for the two-photon state can be obtained using justified approximations. In particular, the thin-crystal approximation has often been invoked in the engineering of high-dimensional entangled states. Knowledge of the conditions under which the thin-crystal approximation remains valid is essential for the realization of experimental setups. We provide a quantitative guideline on the validity of the thin-crystal approximation in calculating the two-photon spatial state. In particular, we show that the applicability of this regime is related to the focusing parameter ${\overline{w}}_p=w_p/\sqrt{{\lambda }_{p}L}$, where $w_p$ and ${\lambda }_p$ are the beam waist and wavelength of the pump beam, respectively, and $L$ is the length of the nonlinear crystal. Additionally, the validity of the thin-crystal regime is investigated concerning the size of a subspace in the Laguerre Gaussian basis, into which the two-photon state can be projected in a given experiment.

We propose a domino-cooling method to realize simultaneous ground-state cooling of a coupled mechanical-resonator chain through an optomechanical cavity working in the unresolved-sideband regime. This domino-effect cooling is realized by combining the cold-damping feedback on the first mechanical resonator with nearest neighbor couplings between other neighboring mechanical resonators. We obtain analytical results for the effective susceptibilities, noise spectra, final mean phonon numbers, and cooling rates of these mechanical resonators, and find the optimal cooling condition for these resonators. In particular, we analyze a two-mechanical-resonator case and find that by appropriately engineering either the laser power or the feedback, a flexible switch between symmetric and asymmetric ground-state cooling can be achieved. This could be used for preparing symmetric quantum states in multimode mechanical systems. We also simulate the cooling performance of a coupled $N$-mechanical-resonator chain and confirm that these resonators can be simultaneously cooled to their quantum ground states in the unresolved-sideband regime. Under proper parameter conditions, the cooling of the mechanical-resonator chain shows a temperature gradient along the chain. This study opens a route to quantum manipulation of multiple mechanical resonators in the bad-cavity regime.

We theoretically study the role of the exceptional point (EP) in a non-Hermitian cavity magnomechanical (CMM) system, with a tunable dissipative magnon-photon coupling. We find that the EP emerging in such a system can radically change the properties of photons and phonons. As a result, flexible on-off optical transmission, coherent switching of slow and fast lights, and enhanced mechanical cooling deep into the ground state can be achievable by approaching the EP. Detailed comparisons between this system and its Hermitian counterpart are given. Our results show that EP-assisted CMM devices can serve as tools for applications in optical communications and electromechanical switching or sensing.

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been used to define the list of TOP500 supercomputers since the debut of the list in 1993. We propose that a similar benchmark, called the quantum LINPACK benchmark, could be used to measure the whole machine performance of quantum computers. The success of the quantum LINPACK benchmark should be viewed as the minimal requirement for a quantum computer to perform a useful task of solving linear algebra problems, such as linear systems of equations. We propose an input model called the Random Circuit Block-Encoded Matrix (RACBEM), which is a proper generalization of a dense random matrix in the quantum setting. The RACBEM model is efficient to be implemented on a quantum computer and can be designed to optimally adapt to any given quantum architecture, with relying on a black-box quantum compiler. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks relevant to many physical applications, such as computing spectral measures, time series generated by a Hamiltonian simulation, and thermal averages of the energy. We implement these linear algebra operations on IBM Q quantum devices as well as quantum virtual machines, and demonstrate their performance in solving scientific computing problems.

Quantum illumination is the task of determining the presence of an object in a noisy environment. We determine the optimal continuous-variable states for quantum illumination in the limit of zero object reflectivity. We prove that the optimal single-mode state is a coherent state, while the optimal two-mode state is the two-mode squeezed-vacuum state. We find that these probes are not optimal at nonzero reflectivity, but remain near optimal. This demonstrates the viability of the continuous-variable platform for an experimentally accessible, near optimal quantum illumination implementation.

We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have an internal memory. Given a collection of candidate processes, our task is to find a discrimination strategy, which may be adaptive and/or entanglement assisted, that maximizes a given objective function subject to given constraints. Our problem can be formulated as a convex problem. Its Lagrange dual problem with no duality gap and necessary and sufficient conditions for an optimal solution are derived. We also show that if a problem has a certain symmetry and at least one optimal solution exists, then there also exists an optimal solution with the same type of symmetry. A minimax strategy for a process discrimination problem is also discussed. As applications of our results, we provide some problems in which an adaptive strategy is not necessary for optimal discrimination. We also present an example of single-shot channel discrimination for which an analytical solution can be obtained.

Quasar absorption spectral data indicate the presence of a spatial gradient in the electromagnetic fine-structure constant $\alpha$ on cosmological length scales. We point out that experiments with accelerometers, including torsion pendula and atom interferometers, can be used as sensitive probes of cosmological spatial gradients in the fundamental constants of nature, which give rise to equivalence-principle-violating forces on test masses. Using laboratory data from the Eöt-Wash experiment, we constrain spatial gradients in $\alpha$ along any direction to be $|\mathbf{\nabla }\alpha /\alpha |<6.6\times {10}^{-4}{\left(\text{Glyr}\right)}^{-1}$ at $95\%$ confidence level. Our result represents an order of magnitude improvement over laboratory bounds from clock-based searches for a spatial gradient in $\alpha$ directed along the observed cosmological $\alpha$-dipole axis. Improvements to accelerometer experiments in the foreseeable future are expected to provide sufficient sensitivity to test the cosmological $\alpha$ dipole seen in astrophysical data.

Focused laser fields with textured polarization on a subwavelength scale allow extracting information on electronic processes which are not directly accessible by homogeneous fields. Here we consider photoionization in radially and azimuthally polarized laser fields and show that, due to the local polarizations of the transversal and the longitudinal laser electric field components, the detected photoelectron spectra depend on the atom position from which the electron originates. The calculation results show the angular dependence of the photoionization amplitude, the quantum phase, and the time delay of the valence shell electrons as the parent atom's position varies across the laser spot. We discuss the possibility of using the photoelectron spectra to identify the position of the ionized atom within the laser spot on the subwavelength scale. The proposal and its illustrations underline the potential for the detection of the atomic position based on attosecond streaking methods.

Laser streaking of photoelectrons has been a well-established technique to extract ultrafast information. In analogy to the streaking of photoelectrons, in this paper, we study the laser streaking of nuclei by numerically simulating the time-dependent Schrödinger equations of ${\mathrm{D}}_2^{+}$ in strong laser fields. We first demonstrate the nuclear streaking, where the dissociating wave packet excited by an isolated attosecond pulse and propagating on molecular potential surfaces is streaked by a strong midinfrared laser pulse. Subsequently, we use an attosecond pulse train composing two successive attosecond pulses to initiate the dissociation of ${\mathrm{D}}_2^{+}$. Depending on the time delay between the attosecond pulse train and the midinfrared laser pulse, the streaked nuclear wave packets show a novel delay-dependent interference pattern. By tracing the wave-packet evolution in the adiabatic presentation, the complicated dissociation pathways are revealed. Based on the streaked nuclear pattern, one may conceive a strategy to probe the real-time nuclear streaking process and extract instantaneous dynamics information experimentally.

For the high-order harmonic generation (HHG) from solids, the dephasing process induced by many-body interactions has been discussed extensively in the studies of using the semiconductor Bloch equations (SBEs). However, the role of dephasing in solid HHG is always ignored in the simulations of using a time-dependent Schrödinger equation under the independent electron approximation. To solve this problem, we introduce the imaginary potential to phenomenologically depict the dephasing process in the solid HHG. Compared with the results of experiment and SBEs, the validity of this approach has been verified by the laser intensity- and wavelength-dependent HHG spectra. Diffusion of the quantum wave packet controls the time-frequency characteristic in solid HHG. To obtain semiclassical trajectories whose predictions are consistent with the quantum simulations, we propose an open-trajectory model by relaxing the zero displacement condition in the tunneling and recollision steps. In addition, the quantum decoherence adjusts the chirp of the emission time profile via modulating the coherent overlap between recombined wave packets, which further paves a way to generate an attosecond pulse from solids and probe the dephasing time via the high-harmonic spectroscopy.

A near-infrared laser pulse generates lasing of $\mathrm{N}{{}_2}^{+}$ during filamentation, while the underlying mechanism of optical gain is still under debate. Here, we study the rotational lasing spectra by manipulating the polarization properties of the pump laser with the polarization gating (PG) method. The independent enhancement of lasing emission was observed in the $P$ branch when the pump laser was modulated by linear polarization gating (LPG). The increased gain is attributed to the promoted population inversion degree between rotational states located on the $B^2{\mathrm{\Sigma }}_u^{+}(v=0)$ and $X^2{\mathrm{\Sigma }}_g^{+}(v=0)$ states. Based on a stimulated emission mechanism, we simulated the lasing spectra and population distributions on the rotational states. The results suggest that the rotational inversion-induced lasing emission mainly contributes to the $P$ branch, which agrees well with the experimental observations.

We theoretically investigate the optical focusing of a rubidium Bose-Einstein condensate onto a planar surface. Our analysis uses a Gaussian variational method that includes the effects of two-body atom-atom interactions and three-body recombination losses. The essential factors such as the width, peak density, and atom loss rate of the focused BEC profile on the surface are investigated and compared to Gross-Pitaevskii numerical simulations. We find a reasonable agreement in the results between our analytical approach and the numerical simulations. Our analysis predicts that condensates of ${10}^5$ atoms could be focused down to $\sim$10 nm widths, potentially allowing nanometer-scale atomic deposition with peak densities greater than ${10}^5$ atoms/$\mu {\mathrm{m}}^2$.

We report the measurement of the Rydberg excitation spectrum by two-photon process in ultracold ${}^{40}\mathrm{K}$ Fermi gases. Two different methods are employed to measure the Rydberg excitation spectrum, depending on the power of the probe laser. One scheme is to reduce atomic losses by means of electromagnetically induced transparency. The other is to enhance the atomic losses by spontaneous avalanche ionization due to the strong Rydberg-Rydberg interactions. We verify the consistency of both of the methods. The highest Rydberg states detectable in our experiment are limited to $n\le 62$ due to the competition between the long Rydberg blockade effective range and the limited atomic cloud size.

We consider a two-component Fermi gas with a contact interaction from the BCS regime to the unitary limit. Starting from the idea that many-body effects should not depend on short-distance or high-momentum physics which is encoded in the $s$-wave scattering length, but only on momentum scales of the order of the Fermi momentum, we build effective low-momentum interactions that reproduce the scattering phase shifts of the contact interaction below some momentum cutoff. Inspired by recent successes of this method in nuclear structure theory, we use these interactions to describe the equation of state of the Fermi gas in the framework of Hartree-Fock-Bogliubov theory with perturbative corrections. In the BCS regime, there is a range of cutoffs where we obtain fully converged results. Near unitarity, convergence is not yet reached, but we obtain promising results for the ground-state energies close to the experimental ones. Limitations and possible extensions of the approach are discussed.