Bell's theorem states that no local hidden-variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden-variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett's nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled ${}^{13}\mathrm{C}$ nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than four and seven standard deviations for six and eight measurement settings, respectively. Our experimental results are in full agreement with quantum predictions and violate Leggett's nonlocal hidden-variable inequality with a high level of confidence.

Interaction between a quantum system and its environment can induce stationary coherences—off-diagonal elements in the reduced system density matrix in the energy eigenstate basis—even at equilibrium. This work investigates the “quantumness” of such phenomena by examining the ability of classical and semiclassical models to describe equilibrium stationary coherence in the multilevel spin boson model, a common model for light-harvesting systems. A well justified classical harmonic-oscillator model is found to fail to capture equilibrium coherence. This failure is attributed to the effective weakness of classical system-bath interactions due to the absence of a discrete system energy spectrum and, consequently, of quantized shifts in oscillator coordinates. Semiclassical coherences also vanish for a dimeric model with parameters typical of biological light harvesting, i.e., where both system sites couple to the bath with the same reorganization energy. In contrast, equilibrium coherence persists in a fully quantum description of the same system, suggesting a uniquely quantum-mechanical origin for equilibrium stationary coherence in, e.g., photosynthetic systems. Finally, as a computational tool, a perturbative expansion is introduced that, at third order in $\hslash$, gives qualitatively correct behavior at ambient temperatures for all configurations examined.

This paper shows that it is possible to piggyback classical information on a stream of qubits protected by quantum error-correcting codes. The piggyback channel can be created by introducing intentional errors corresponding to a controlled sequence of syndromes. These syndromes are further protected, when quantum noise is present, by classical error-correcting codes according to a performance-delay trade-off. Classical information can thus be added and extracted at arbitrary epochs without consuming additional quantum resources and without disturbing the quantum stream.

The study of low-temperature hydrogen plasmas is relevant for many technological plasma applications. The theoretical investigation of elementary processes, especially those involving H, D, and T species, is crucial for the modeling of nonequilibrium plasma systems such as those found in fusion plasmas. We report fully quantum time-independent calculations of rate coefficients for the vibrationally inelastic and reactive collisions of T with ${\mathrm{D}}_2(v=0)$ and of D with ${\mathrm{T}}_2(v=0)$. Our calculations are based on the ${\mathrm{H}}_3$ global potential-energy surface of Mielke et al. [S. L. Mielke et al., J. Chem. Phys. 116, 4142 (2002)]. We obtain state-to-state rate coefficients for the formation of DT through $\mathrm{T}+{\mathrm{D}}_2$ and $\mathrm{D}+{\mathrm{T}}_2$ reactions and for the vibrational excitation of ${\mathrm{D}}_2$ by T and of ${\mathrm{T}}_2$ by D for temperatures up to 2500 K. The results are compared to existing ones for other hydrogen isotopes and significant differences are found between the different sets of results, confirming that specific data have to be obtained for all the collisional systems of interest of hydrogen plasmas. We expect that this data will allow a more accurate modeling of hydrogen plasmas of interest for technological applications.

We develop a systematic approach to derive narrowband (NB) and passband (PB) composite sequences which can produce any preselected transition probability with any desired accuracy. The NB composite pulses are derived by successive cancellation of derivative terms in the propagator. The PB pulses are built by combining two $\pi /2$ NB pulses. Both the NB and the PB pulses feature vanishing wings on both sides of the central region around the target transition probability, and the PB pulses offer also a flat (broadband) top around the target probability. The NB sequences are particularly suitable for sensing and metrology applications, whereas the PB sequences can be very useful for qubit control in the case of tightly spaced laser-driven qubits for they ensure both selectivity (suppressed cross talk to neighbors) and robustness (suppressed laser pointing instability). Other possible applications include selective (NB) or both selective and robust (PB) control of close transitions in frequency space.

We analyze zero-temperature universal properties of the simplest Galilean-invariant model of spinless low-dimensional fermions with short-range two-body interactions. In particular, it is shown that after proper renormalization of the coupling constant, even the dilute system possesses a rich phase diagram that includes the superfluid state and the metastable “upper-branch” behavior.

Nuclear-magnetic-resonance gyroscopes that detect rotation as a shift in the precession frequency of nuclear spins have attracted a lot of attention. Under a feedback-generated drive, the precession frequency in the steady state is supposed to be dependent only on the angular momentum and an applied magnetic field. However, nuclei with spins larger than 1/2 experience electric quadrupole interaction with electric-field gradients at the cell walls. This quadrupole interaction shifts the precession frequencies of the nuclear spins, which brings inaccuracy to the rotation measurement as the quadrupole interaction constant $C_q$ is difficult to precisely measure. In this paper, the effects of quadrupole interaction on nuclear-magnetic-resonance gyroscopes are theoretically studied. We find that, when the constant $C_q$ is small compared to the characteristic decay rate of the system, which is the case in most gyroscopes for practical use, as the strength of the feedback-driving field increases, the quadrupole shift monotonically decreases, regardless of the system parameters in including $C_q$. Furthermore, the larger driving amplitude can reduce the quadrupole shift's fluctuation caused by fluctuations of the system parameters, and, thus, it can reduce systematic errors resulted from the quadrupole interaction. In the large-$C_q$ regime, more than one precession frequency exists, and the nuclear spins may precess with a single frequency or multifrequencies depending on initial conditions. In this regime with large driving amplitudes, the nuclear spin can restore the single-frequency precession. These results are obtained by solving an effective master equation of the nuclear spins in a rotating frame from which both the steady-state solutions and the dynamics of the system are shown.

The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean-squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.

We proposed a spectroscopic method that extends Ramsey's atomic spectroscopy to detect the transition frequency of a qubit fabricated on a superconducting circuit. The method uses a multi-interval train of qubit biases to implement an alternate resonant and dispersive couplings to an incident probe field. The consequent absorption spectrum of the qubit has a narrower linewidth at its transition frequency than that obtained from constantly biasing the qubit to resonance while the middle dispersive evolution incurs only a negligible shift in detected frequency. Modeling on transmon qubits, we find that the linewidth reduction reaches 23% and Ramsey fringes are simultaneously suppressed at extreme duration ratio of dispersion over resonance for a double-resonance scheme. If the scheme is augmented by an extra resonance segment, a further 37% reduction can be achieved.

Strongly long-range interacting quantum systems—those with interactions decaying as a power law $1/r^{\alpha }$ in the distance $r$ on a $D$-dimensional lattice for $\alpha \le D$—have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\alpha \le D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all $\alpha <D$. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.

In this Rapid Communication, we propose a protocol to reverse a quantum many-body dynamic process. We name it “many-body echo” because the underlying physics is closely related to the spin echo effect in nuclear magnetic resonance systems. We consider a periodical modulation of the interaction strength in a weakly interacting Bose condensate, which resonantly excites quasiparticles from the condensate. A dramatic phenomenon is that, after pausing the interaction modulation for half a period and then continuing on with the same modulation, nearly all the excited quasiparticles in the resonance modes will be absorbed back into the condensate. During the intermediate half-period, the free evolution introduces a $\pi$ phase, which plays a role reminiscent of that played by the $\pi$ pulse in the spin echo. Comparing our protocol with another one implemented by the Chicago group in a recent experiment, we find that ours is more effective at reversing the many-body process. The difference between these two schemes manifests the physical effect of the micromotion in the Floquet theory.

We study the effect of feedback controls in quantum parameter estimation. In particular, we study the estimation of a magnetic field with a spin in the presence of the spontaneous emission where feedback control, triggered by the detection of the emitted photons, is employed to improve the precision limit. We also study the effect of additional Hamiltonian controls and show that they can provide further improvement on the precision limit.

In the scattering and stopping of heavy ions on a few surface layers in solids, contributions of the electronic and nuclear energy losses can become comparable. In this work we present a study of 0.6–5-keV Ar ion scattering on a Cu (100) surface. Energy-loss spectra were measured and displayed some changes as the incident ion energy changes. Thus, a structured spectrum is observed at the higher energies. We analyze the characteristics of the spectra and contributions from the nuclear and electronic energy-loss components using both a Monte Carlo kinetics simulation assuming an averaged electron density and a semiclassical deterministic simulation with an inhomogeneous electron density in the solid. The general features of the experimental spectra were well reproduced, and semiclassical simulations allow us to identify contributions from trajectories coming from below and on top of the surface atomic layer. The relative contribution of nuclear energy loss and electronic energy loss (EEL) were delineated and a more refined analysis of the EEL for different trajectories is presented.

The exchange of off-resonant propagating photons between distant quantum emitters induces coherent interactions among them. The range of such interactions, and whether they are accompanied by dissipation, depends on the photonic energy dispersion, its dimensionality, and/or the light-matter couplings. We characterize the limits of photon-mediated interactions for the case of generic one-dimensional photonic baths under the typical assumptions, i.e., finite range hoppings for the photonic bath plus local and rotating-wave light-matter couplings. In that case, we show how, irrespective of the system's parameter, the coherent photon-mediated interactions can always be written as a finite sum of exponentials and thus cannot display a power-law asymptotic scaling. As an outlook, we show how by relaxing some of these conditions, e.g., going beyond local light-matter couplings (e.g., giant atoms) or with longer-range photon hopping models, power-law interactions can be obtained within certain distance windows or even in the asymptotic regime for the latter case.

Higher-order topological insulators not only exhibit the exotic bulk-boundary correspondence principle but also have an important application in quantum computing. However, it seems they have not been achieved in the discrete-time quantum walk. In this paper we construct a two-dimensional coinless discrete-time quantum walk to simulate the second-order topological insulator with zero-dimensional corner states. We show that both of the corner and edge states can be observed through the probability distribution of the walker after a multistep coinless discrete-time quantum walk. Finally, we propose a possible experimental implementation to realize this coinless discrete-time quantum walk in a three-dimensional integrated photonic circuit and verify the robustness of the corner states against the small disorder. Our work offers an alternative route to explore exotic higher-order topological matters using discrete-time quantum walks.

The uncertainty principle is a striking and fundamental feature in quantum mechanics, distinguishing it from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a particle. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. Here, we present an improvement of the tripartite quantum-memory-assisted entropic uncertainty relation. The uncertainty's lower bound is derived by considering mutual information and the Holevo quantity. It shows that the bound derived by this method will be tighter than the lower bound of Renes and Boileau [Phys. Rev. Lett. 103, 020402 (2009)]. Furthermore, regarding a pair of mutual unbiased bases as the incompatibility, our bound will become extremely tight for the three-qubit $X$-state system, completely coinciding with the entropy-based uncertainty, and can restore Renes and Boileau's bound with respect to arbitrary tripartite pure states. In addition, by applying our lower bound one can attain the tighter bound of the quantum secret key rate, which is of basic importance to enhance the security of quantum key distribution protocols.

One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, although the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four-state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four-dimensional coin Hilbert space. The well-known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such an escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the two-dimensional square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or nonexistence of the escaping state and the area covered by the spreading wave packet.

We investigate the dynamics of a spin chain with Kitaev-type interaction in a transverse magnetic field, for both a constant field and a periodically kicked field. We investigate analytically the revivals in the dynamical behavior of the magnetization, and measures of local quantum correlations, the concurrence measure of the entanglement, and the quantum discord. The magnetization revivals are seen even for larger chain lengths, with reduced revival peaks, both near and away from the critical point at zero magnetic field. The quantum entanglement and correlation measures, contrary to the expected behavior, exhibit reduced quantum correlations in the critical region, compared to the region away from the critical point. The concurrence is larger than the quantum discord away from the critical region. The pair entanglement is near zero for all times in the critical region, though the quantum discord is nonzero, capturing the underlying diagonal correlations. The kicked magnetic field dynamics shows similar evolution for the magnetization and quantum correlations. For special values of the kicking period, the concurrence shows alternates between zero and nonzero values for successive kicks in the noncritical region.

We study the entanglement distillation in continuous-variable systems when a photon replacement protocol is employed. A cascaded protocol is studied and we find that the resultant entanglement increases by increasing the number of repetitions. Interestingly, the entanglement enhancement is not sensitive to the asymmetry of the protocol and gives the same result for any arrangement in the absence of loss. The non-Gaussianity of the outcome state is also studied and it is found that the non-Gaussianity of the state dramatically depends on the experimental arrangements. We also consider the case of imperfect detectors and show that the main results are valid provided high-efficiency detectors are employed. By providing practical information on photon replacement operation, this work is one step towards the realization of universal quantum computation; in particular, in setups where de-Gaussifying protocols are only applicable to one of the parties.