We introduce a method for testing quantum correlations in terms of quasiprobability functions in the presence of noise. We analyze the effects of measurement imperfection and thermal environment on quantum correlations and show that their noise effects can be well encapsulated into the change of the order parameter of the generalized quasiprobability function. We then formulate a noise-adaptive entanglement witness in the form of a Bell-type inequality by using the generalized quasiprobability function. Remarkably, it allows us to observe quantum correlations under severe noise. Our method provides a useful tool to test quantum correlations in near-term noisy quantum processors with continuous-variable systems.

Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. We apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert-Schmidt distance does not form a proper entanglement measure, it can nevertheless be useful for witnessing entanglement. We provide a few methods based on the Gilbert's algorithm that can reliably qualify a given state as strongly entangled or practically separable, while being computationally efficient. The method also outputs successively improved approximations to the closest separable state for the given state. We demonstrate the efficacy of the method with examples.

The electronic stopping power for low-velocity ions (including protons and $\alpha$ particles) in the semiconductor Ge is investigated with the aid of time-dependent density functional theory based on Ehrenfest dynamics. The purpose of this study is to further learn about the energy loss mechanisms of the slow ions. When the projectile ions pass through the crystal film along the $〈100〉, 〈110〉$, and $〈111〉$ channels, we analyze the channeling effect of the electronic stopping power in detail by investigating the channeling electronic density, the stopping force, and the trapped electrons. Our results are in good agreement with the available experimental data and the other theoretical calculations, which demonstrate that this approach is able to reasonably describe the electronic stopping power. Furthermore, these results can act as the reference data for the ion-beam irradiation of Ge in the low-energy regime.

We report on measurements of the $5S\text{−}6P$ rubidium transition frequencies for rubidium isotopes with an absolute uncertainty of $\le 20\mathrm{kHz}$ for the $5S\to 6P_{3/2}$ transition and better than $20\mathrm{MHz}$ for the $5S\to 6P_{1/2}$ transition, achieved by saturated absorption spectroscopy. From the results we derive the hyperfine splitting with an accuracy of $30\mathrm{kHz}$ and $450\mathrm{kHz}$, respectively. This is an improvement of two orders of magnitude for the $5S\to 6P_{3/2}$ transition to the current state of the art. We also verify the literature values for the $5S\to 6P_{1/2}$ transition, the isotope shifts, as well as the magnetic dipole constants and the electric quadrupole constants.

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultracold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work allows for subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

We have developed a theory for the Kerr nonlinearity in nanohybrids made of an ensemble of metallic nanoshells and low concentration of quantum emitters. A metallic nanoshell is made of a metallic core sphere and dielectric shell. We consider that quantum emitters are four-level quantum systems. When a probe laser light falls in the metallic nanoshells, the surface plasmon polariton electric field is produced at the interface between the metal sphere and dielectric shell. This electric field along with the probe field induces dipoles in metallic nanoshells. These dipoles interact with each other via the dipole-dipole interaction. The Kerr nonlinearity has been calculated by using the quantum density matrix method in the presence of the dipole-dipole interaction (coupling). We found that in the weak-coupling limit there is an enhancement in the Kerr nonlinearity. On the other hand, in the strong-coupling limit, the peaks in the Kerr coefficient split from two peaks to four peaks when the frequency of the dipole electric field is in the resonance with the exciton frequency. The splitting in the spectrum is due to the presence of the dressed sates created in the system. We showed that heights and locations of peaks are very sensitive to the strength of the dipole-dipole interaction. Physics of the enhancement can be used fabricate Kerr nanosensors. On the other hand, physics of the splitting from two peaks (ON) to four peaks (OFF) can be used to fabricate Kerr nanoswitches.

We performed measurements of the photon correlation $\left[g^{\left(2\right)}\left(\tau \right)\right]$ in driven nonlinear high-$Q$ silicon photonic crystal microcavities. The measured $g^{\left(2\right)}\left(\tau \right)$ exhibits damped oscillatory behavior when the input pump power exceeds a critical value. From a comparison between experiments and simulations, we attribute the measured oscillation of $g^{\left(2\right)}\left(\tau \right)$ to self-pulsing (a limit cycle) emerging from an interplay between the photon, carrier, and thermal dynamics. Namely, the oscillation frequency of $g^{\left(2\right)}\left(\tau \right)$ corresponds to the oscillation period of the limit cycle, while its finite coherence (damping) time originates from the stochastic nature of the limit cycle. From the standpoint of phase reduction theory, we interpret the measured coherence time of $g^{\left(2\right)}\left(\tau \right)$ as the coherence (diffusion) time of a generalized phase of the limit cycle. Furthermore, we show that an increase in laser input power enhances the coherence time of $g^{\left(2\right)}\left(\tau \right)$ up to the order of microseconds, which could be a demonstration of the stabilization of a stochastic limit cycle through pumping.

In the present work, a traditional quantity, the averaged fidelity, is introduced as the steering parameter. From the definitions of steering from Alice to Bob and the joint measurability, a general scheme is developed to design linear steering criteria. For a given set of measurements on Bob's side, the so-called nonsteering threshold is defined to quantify the ability to detect steering. If the measured averaged fidelity exceeds this threshold, it is shown that the state shared by Alice and Bob is steerable from Alice to Bob, and the measurements performed by Alice are also verified to be incompatible. Within the general scheme, a discussion about how to design optimal criteria is provided for two different scenarios: (a) to find the optimal measurements on Bob's side when the state is unknown and (b) to find the optimal measurements for Alice when the state and the measurements on Bob's side are given.

As the minituarization of electronic devices, which are sensitive to temperature, grows apace, sensing of temperature with ever smaller probes is more important than ever. Genuinely quantum mechanical schemes of thermometry are thus expected to be crucial to future technological progress. We propose an alternative method to measure the temperature of a bath using the weak measurement scheme with a finite-dimensional probe. The precision offered by the present scheme not only shows similar qualitative features as the usual quantum-Fisher-information-based thermometric protocols, but also allows for flexibility over setting the optimal thermometric window through the judicious choice of postselection measurements.

One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of quantum mechanics within a general epistemic framework based on an operational scheme of estimation of momentum given information on the conjugate positions under epistemic restriction. The epistemic restriction is parameterized by a global-nonseparable random variable on the order of Planck constant, an ontic extension to the separable classical phase-space variables. Within the estimation scheme, the canonical quantum laws are reconstructed for a specific estimator and estimation error. In the present work, keeping the Born's quadratic law intact, we construct a class of nonlinear variants of Schrödinger equation and generalized Heisenberg uncertainty principle within the estimation scheme by assuming a more general class of estimation errors. The nonlinearity of the Schrödinger equation and the deviation from the Heisenberg uncertainty principle thus have a common transparent operational origin in terms of generalizations of estimation errors. We then argue that a broad class of nonlinearities and deviations from the Heisenberg uncertainty principle arise from estimation errors violating a plausible inferential-causality principle of estimation independence which is respected by the standard quantum mechanics. This result therefore constrains possible extensions of quantum mechanics and suggests directions to generalize quantum mechanics which comply with the principle of estimation independence.

The generalized amplitude-damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analog of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is antidegradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in Rosati et al., [Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.

We propose an $E$-truncated $K$-moment and semidefinite relaxations (ETKM-SDR) method to check whether an $m$-partite quantum mixed state is separable and give a decomposition for it if it is. We first convert the separability discrimination problem of mixed states to the positive Hermitian decomposition problem of Hermitian tensors. Then, employing the $E$-truncated $K$-moment method, we obtain an optimization model for discriminating separability. Moreover, by applying the semidefinite relaxation method, we get a hierarchy of semidefinite relaxation optimization models and propose an algorithm for detecting the separability of mixed states. The algorithm can also be used for symmetric and nonsymmetric decomposition of separable mixed states. By numerical examples, we find that not all symmetric separable states have symmetric decompositions.

Certain quantum states are well known to be particularly fragile in the presence of decoherence, as illustrated by Schrödinger's famous gedanken cat experiment. More recently it has been considered that quantum states can be characterized through a hierarchy of quantum quantities such as entanglement, quantum correlations, and quantum coherence. It has been conjectured that each of these quantities has various degrees of fragility in the presence of decoherence. Here we experimentally confirm this conjecture by preparing tripartite photonic states and subjecting them to controlled amounts of dephasing. When the dephasing is applied to all the qubits, we find that the entanglement is the most fragile quantity, followed by the quantum coherence and then mutual information. This is in agreement with the widely held expectation that multipartite quantum correlations are a highly fragile manifestation of quantumness. We also perform dephasing on one of the three qubits on star and $W\overline{W}$ states. Here the distribution of the correlations and coherence in the star state becomes more important in relation to the dephasing location.

This paper presents a method to convert position correlation of photon pairs into polarization entanglement. This is achieved by individually manipulating the polarization state of photons generated in different parts of a nonlinear medium and coherently superposing them. This concept is experimentally demonstrated using photon pairs produced by spontaneous parametric down-conversion. The method is used to implement a compact source producing an observed photon-pair rate of $120000{\text{s}}^{-1}/\text{mW}$ with an entanglement fidelity of $0.991\pm 0.013$. This method can be extended to any photon-pair generation process with initial position correlation.

Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and quantum-state tomography. In this work, we calculate exact and compact results for the mean-square Hilbert-Schmidt distance between a random density matrix and a fixed density matrix, and also between two random density matrices. In the course of derivation, we also obtain corresponding exact results for the distance between a Wishart matrix and a fixed Hermitian matrix, and two Wishart matrices. We verify all our analytical results using Monte Carlo simulations. Finally, we apply our results to investigate the Hilbert-Schmidt distance between reduced density matrices generated using coupled kicked tops.

A Bernoulli factory is a model of randomness processing. Recently, the quantum generalization of a Bernoulli factory with a quantum input and classical output offers a clear advantage over classical means in simulating classical randomness. A more “quantum” version of a Bernoulli factory with a quantum input and quantum output has been proposed and shows applications in simulating quantum randomness using quantum resources, the so-called quantum-to-quantum Bernoulli factory, which simulates probability amplitudes rather than probability. In this paper, we report an experimental implementation of a quantum-to-quantum Bernoulli factory with linear optics. We implement three elements of a quantum-to-quantum Bernoulli factory, including inversion, multiplication, and addition, and demonstrate how to compare quantum states via a quantum-to-quantum Bernoulli factory. Our results provide a thorough understanding of the Bernoulli factory problem in the quantum world and will stimulate the quantum advantages in simulating a wider range of classically infeasible random processes.

Here we propose an effective scheme to realize robust quantum state transfer (QST) with the topologically protected channel in a superconducting flux qubit chain. Based on the constructed Su-Schrieffer-Heeger model, bidirectional QST between the two ends of the channel can be realized with a high fidelity. Remarkably, we design a switch mechanism of the QST channel by appropriately introducing the on-site defect on the qubit chain. Under this mechanism, we can control robust quantum information transmission or storage and even generate a new state transfer channel.

Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman et al. [Phys. Rev. A 64 012310 (2001)]. We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how single-qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in circuit-like and measurement-based architectures.