We analyze the connection between Bell inequality violations and symmetric extendibility of quantum states. We prove that 2-qubit reduced states of multiqubit symmetric pure states do not violate the Bell Clauser-Horne-Shimony-Holt (CHSH) inequality. We then prove the more general converse that any 2-qubit state that violates the CHSH inequality cannot have a symmetric extension. We extend our analysis to qudits and provide a test for symmetric extendibility of 2-qudit states. We show that if a 2-qudit Bell inequality is monogamous, then any 2-qudit state that violates this inequality does not have a symmetric extension. For the specific case of 2-qutrit states, we use numerical evidence to conjecture that the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the nonexistence of its symmetric extension.

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time $\text{poly}({log}_2\left(N\right),d,\kappa ,1/\epsilon )$, where $N$ is the size of the data set, $d$ is the number of adjustable parameters, $\kappa$ is the condition number of the design matrix, and $\epsilon$ is the desired precision in the output. We also show that the polynomial dependence on $d$ and $\kappa$ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Genuine multipartite entanglement has been found in some spin chain systems. However, genuine multipartite nonlocality is much rarer than genuine multipartite entanglement. Here we present genuine multipartite nonlocality in a spin chain system. After introducing the definition of genuine multipartite nonlocality and a multipartite Bell-type inequality, we construct a group of joint measurements for the inequality in a one-dimensional ferromagnetic $N$-qubit chain with nearest-neighbor $XXZ$ interaction, and many violations to the inequality have been found. The violations do indicate that genuine multipartite nonlocality exists in this ferromagnetic spin-1/2 chain system. Last but not least, we also calculate genuine multipartite entanglement concurrence in the same spin chain to demonstrate the difference and relationship between genuine multipartite nonlocality and genuine multipartite entanglement.

We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios: In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady-state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $\mathrm{\Lambda }$-type atoms. However, at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here, we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.

We study the entanglement between two identical two-level atoms located near an ideal model of invisibility cloaks by monitoring the time evolution of the concurrence measure. We obtain the reduced density operator of the atomic subsystem based on a canonical quantization scheme presented for the electromagnetic field interacting with atomic systems in the presence of an anisotropic, inhomogeneous, and absorbing magnetodielectric medium. It is shown that two atoms, which are prepared initially in an unentangled state, are correlated in the weak coupling regime via the spontaneous emission and the dipole-dipole interaction of two atoms mediated by the invisibility cloak. We therefore find that the invisibility cloak, independent of the hidden object, works fairly well at frequencies far from the resonance frequency of the object and the cloak, whereas near the resonance frequency the hidden object becomes detectable due to a sharp reduction of the concurrence.

We consider two qubits undergoing local dissipation and subject to local driving. We then determine the optimal Markovian feedback action to preserve initial entanglement as well as to create stationary entanglement with the help of an $\text{XY}$ interaction Hamiltonian. Such feedback actions are worked out in a way not depending on the initial two-qubit state, whence called universal.

The quantum coherence of one-dimensional planar spin models with Dzyaloshinsky-Moriya interaction is investigated. The anisotropic XY model, the isotropic XX model, and the transverse field model are studied in the large $N$ limit using two qubit reduced density matrices and two point correlation functions. From our investigations we find that the coherence as measured using Jensen-Shannon divergence can be used to detect quantum phase transitions and quantum critical points. The derivative of coherence shows nonanalytic behavior at critical points, leading to the conclusion that these transitions are of second order. Further, we show that the presence of Dzyaloshinsky-Moriya coupling suppresses the phase transition due to residual ferromagnetism, which is caused by spin canting.

We calculate the quantum heat generation, the interaction force, and the frictional torque for two rotating spherical nanoparticles with a radius $R$. In contrast to the static case, when there is an upper limit in the radiative heat transfer between the particles, for two rotating nanoparticles the quantum heat generation rate diverges when the angular velocity becomes equal to the poles in the photon emission rate. These poles arise for the separation $d<d_0=R{[3/{\varepsilon }^{″}\left({\omega }_0\right)]}^{1/3}$ [where ${\varepsilon }^{″}\left({\omega }_0\right)$ is the imaginary part of the dielectric function for the particle material at the surface phonon or plasmon polariton frequency ${\omega }_0$] due to the anomalous Doppler effect and the mutual polarization of the particles and they exist even for the particles with losses. Similar singularities exist also for the interaction force and the frictional torque. The obtained results can be important for biomedical applications.

We study superadiabatic quantum control of a three-level quantum system whose energy spectrum exhibits multiple avoided crossings. In particular, we investigate the possibility of treating the full control task in terms of independent two-level Landau-Zener problems. We first show that the time profiles of the elements of the full control Hamiltonian are characterized by peaks centered around the crossing times. These peaks decay algebraically for large times. In principle, such a power-law scaling invalidates the hypothesis of perfect separability. Nonetheless, we address the problem from a pragmatic point of view by studying the fidelity obtained through separate control as a function of the intercrossing separation. This procedure may be a good approach to achieve approximate adiabatic driving of a specific instantaneous eigenstate in realistic implementations.

Molecular orientation has wide applications in physics and chemistry. However, the degree of orientation achieved in experiments is difficult to evaluate, especially when three-dimensional (3D) orientation is involved. We show numerically and analytically that odd-even high-harmonic generation (HHG) from asymmetric molecules is sensitive to both the degree of orientation and the molecular structure. Based on the observations, a simple procedure is proposed to probe the degree of orientation with odd-even HHG, without the need of solving the rotational equation. This procedure can be applied to 3D-oriented top molecules such as polar or nonpolar planar ${\mathrm{H}}_3{}^{2+}$ with high resolution.

We report the trapping of ultracold ${}^{87}\mathrm{Rb}$ atoms in a 0.7-$\mu \text{m}$-period two-dimensional triangular magnetic lattice on an atom chip. The magnetic lattice is created by a lithographically patterned magnetic Co/Pd multilayer film plus bias fields. Rubidium atoms in the $|F=1,m_F=-1\rangle$ low-field seeking state are trapped at estimated distances down to about $100\mathrm{nm}$ from the chip surface and with calculated mean trapping frequencies up to about $800\mathrm{kHz}$. The measured lifetimes of the atoms trapped in the magnetic lattice are in the range 0.4–$1.7\mathrm{ms}$, depending on distance from the chip surface. Model calculations suggest the trap lifetimes are currently limited mainly by losses due to one-dimensional thermal evaporation following loading of the atoms from the $Z$-wire trap into the very tight magnetic lattice traps, rather than by fundamental loss processes such as surface interactions, three-body recombination, or spin flips due to Johnson magnetic noise. The trapping of atoms in a $0.7\text{−}\mu \mathrm{m}$-period magnetic lattice represents a significant step toward using magnetic lattices for quantum tunneling experiments and to simulate condensed matter and many-body phenomena in nontrivial lattice geometries.

We study the effect of unidirectional reflection in the bilayer optical model with the balanced loss and gain terms. It was found that if the impedances characterizing the scattering part are different from those describing the leads, an effect of switching of unidirectional reflection emerges. In this case the vanishing reflection occurs both for the left and for the right incident wave, depending on the wave frequency. It is shown that the alternation of the unidirectional reflection from the left to the right can occur even if the corresponding Hamiltonian is non-$\mathcal{P}\mathcal{T}$-symmetric. Our analytical results are demonstrated by numerical data.

We propose a scheme for simulating the behaviors of Weyl semimetals by using a two-dimensional array of degenerate optical cavities. To simplify such a three-dimensional system to a two-dimension system, the orbital angular momentum of the light is used to support an extra synthetic dimension. We find that this system is quite suitable for the purpose of investigating the features of the Weyl point by taking advantage of the input-output relation of the optical cavity system. We show that the transport properties of our system are determined by the number of sites along the constrained direction and the spin texture of the system makes the transport momentum dependent and spin dependent.

It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the Su-Schrieffer-Heeger (SSH) system can be simulated, which exhibits states of nonzero winding number and has topologically protected boundary states. In the large-system limit this approach uses quadratically fewer resources to carry out quantum simulations than previous linear-optical approaches and can be readily generalized to higher-dimensional systems. The basic optical units that implement this simulation consist of combinations of optical multiports that allow photons to reverse direction.

In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half-wave plate, and a quarter-wave plate, as well as an implementation of cnot and Pauli gates, by using two atoms confined in a two-dimensional plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we consider two trapped atoms and let only one of them interact simultaneously with two circularly polarized Laguerre-Gaussian beams.

We study the coherent transport of a single photon, which propagates in a one-dimensional waveguide and is scattered by a quadratic optomechanical system. Our approach, which is based on the Lippmann-Schwinger equation, gives an analytical solution to describe the single-photon transmission and reflection properties. We analyze the transport spectra and find they are not only related to the optomechanical system's energy-level structure, but also dependent on the optomechanical system's inherent parameters. For the existence of atomic degrees of freedom, we get a Rabi-splitting-like or an electromagnetically induced transparency (EIT)-like spectrum, depending on the atom-cavity coupling strength. Here, we focus on the single-photon strong-coupling regime so that single-quantum effects could be seen.

Phonon blockade is achieved in a quadratically coupled optomechanical system, in which the nonlinear interaction between phonons is induced by a driving field via radiation pressure. It is different from the previous standard methods, where the nonlinear interaction for observing phonon blockade is obtained by coupling the mechanical resonator to a two-level system. The effective coupling strength can be tuned by controlling the amplitudes of the driving field, which allows large nonlinearities for the optomechanical system. The second-order correlation function is discussed both analytically and numerically to characterize the phonon statistical properties and the results show that the phonon blockade is available when the effective coupling strength is larger than the mechanical decay rate. This work provides a possible way to experimentally realize phonon blockade.

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.

The phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates $x\in \mathbb{Z}$. The motion is controlled by a weakly nonlocal $2J$-parametric external potential $V$ which is non-Hermitian but $\mathcal{P}T$ symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to $J=7$.