Bell’s theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions—e.g., locality or measurement independence—have to be relaxed in order to allow for a classical description of such experiments. Here we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality, and bilocality assumptions, to a novel causal interpretation of Clauser-Horne-Shimony-Holt inequality violations.

We analyze the implications of the violations of the strong Huygen’s principle in the transmission of information from the early Universe to the current era via massless fields. We show that much more information reaches us through timelike channels (not mediated by real photons) than is carried by rays of light, which are usually regarded as the only carriers of information.

We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction ($\overline{\mathrm{MS}}$) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the $\overline{\mathrm{MS}}$ quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the $\overline{\mathrm{MS}}$ heavy quark masses.

We show that the inductive coupling between the quantum mechanical motion of a superconducting microcantilever and a flux-dependent microwave quantum circuit can attain the strong single-photon nanomechanical coupling regime with feasible experimental parameters. We propose to use a superconducting strip, which is in the Meissner state, at the tip of a cantilever. A pickup coil collects the flux generated by the sheet currents induced by an external quadrupole magnetic field centered at the strip location. The position-dependent magnetic response of the superconducting strip, enhanced by both diamagnetism and demagnetizing effects, leads to a strong magnetomechanical coupling to quantum circuits.

A quantitative interpretation of the experimentally measured high-pressure plasma response to externally applied three-dimensional (3D) magnetic field perturbations, across the no-wall Troyon $\beta$ limit, is achieved. The self-consistent inclusion of the drift kinetic effects in magnetohydrodynamic (MHD) modeling [Y. Q. Liu et al., Phys. Plasmas 15, 112503 (2008)] successfully resolves an outstanding issue of the ideal MHD model, which significantly overpredicts the plasma-induced field amplification near the no-wall limit, as compared to experiments. The model leads to quantitative agreement not only for the measured field amplitude and toroidal phase but also for the measured internal 3D displacement of the plasma. The results can be important to the prediction of the reliable plasma behavior in advanced fusion devices, such as ITER [K. Ikeda, Nucl. Fusion 47, S1 (2007)].

We report the emergence of a charge-density wave (CDW) in Ca-intercalated bilayer graphene (${\mathrm{C}}_6\mathrm{Ca}{\mathrm{C}}_6$), the thinnest limit of superconducting ${\mathrm{C}}_6\mathrm{Ca}$, observed by low-temperature, high-magnetic-field scanning tunneling microscopy or spectroscopy, and angle-resolved photoemission spectroscopy. While the possible superconductivity was not observed in epitaxially grown ${\mathrm{C}}_6\mathrm{Ca}{\mathrm{C}}_6$ on a SiC substrate, a CDW order different from that observed on the surface of bulk ${\mathrm{C}}_6\mathrm{Ca}$ was observed. It is inferred that the CDW state is induced by the potential modulation due to the commensurate lattice matching between the ${\mathrm{C}}_6\mathrm{Ca}{\mathrm{C}}_6$ film and the SiC substrate.

A combination of femtosecond laser excitation with a low-temperature scanning tunneling microscope is used to study long-range interaction during diffusion of CO on Cu(111). Both thermal and laser-driven diffusion show an oscillatory energy dependence on the distance to neighboring molecules. Surprisingly, the phase is inverted; i.e., at distances at which thermal diffusion is most difficult, it is easiest for laser-driven diffusion and vice versa. We explain this unexpected behavior by a transient stabilization of the negative ion during diffusion as corroborated by ab initio calculations.

We present the first unbiased results for the mobility $\mu$ of a one-dimensional Holstein polaron obtained by numerical analytic continuation combined with diagrammatic and worldline Monte Carlo methods in the thermodynamic limit. We have identified for the first time several distinct regimes in the $\lambda \text{−}T$ plane including a band conduction region, incoherent metallic region, an activated hopping region, and a high-temperature saturation region. We observe that although mobilities and mean free paths at different values of $\lambda$ differ by many orders of magnitude at small temperatures, their values at $T$ larger than the bandwidth become very close to each other.

A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density functional theory. We show that the accurate prediction of strongly bound electron-hole pairs within this framework using simple approximations is still a challenge and that available promising results have to be revisited. Deriving a set of analytical formulas we analyze and explain the difficulties. We deduce an alternative approximation from an iterative scheme guided by previously available knowledge, significantly improving the description of exciton binding energies. Finally, we show how one can “read” exciton binding energies from spectra determined in the random phase approximation, without any further calculation.

The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum spin Hall samples is discussed.

We report a fine tuned doping study of strongly overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.

Low-energy quasiparticle excitations in the superconducting (SC) state of ${\mathrm{UBe}}_{13}$ were studied by means of specific-heat ($C$) measurements in a rotating field. Quite unexpectedly, the magnetic-field dependence of $C(H)$ is linear in $H$ with no angular dependence at low fields in the SC state, implying that the gap is fully open over the Fermi surfaces, in stark contrast to previous expectations. In addition, a characteristic cubic anisotropy of $C(H)$ was observed above 2 T with a maximum (minimum) for $H\parallel [001]$ ([111]) within the ($1\overline{1}0$) plane, in the normal as well as in the SC states. This oscillation possibly originates from the anisotropic response of the heavy quasiparticle bands, and might be a key to understand the unusual properties of ${\mathrm{UBe}}_{13}$.

Heavy-fermion superconductors are prime candidates for novel electron-pairing states due to the spin-orbital coupled degrees of freedom and electron correlations. Superconductivity in ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ discovered in 1979, which is a prototype of unconventional (non-BCS) superconductors in strongly correlated electron systems, still remains unsolved. Here we provide the first report of superconductivity based on the advanced first-principles theoretical approach. We find that the promising candidate is an $s_{\pm }$-wave state with loop-shaped nodes on the Fermi surface, different from the widely expected line-nodal $d$-wave state. The dominant pairing glue is magnetic but high-rank octupole fluctuations. This system shares the importance of multiorbital degrees of freedom with the iron-based superconductors. Our findings reveal not only the long-standing puzzle in this material, but also urge us to reconsider the pairing states and mechanisms in all heavy-fermion superconductors.

A metastable phase $\alpha \text{−}{\mathrm{FeSi}}_2$ was epitaxially stabilized on a silicon substrate using pulsed laser deposition. Nonmetallic and ferromagnetic behaviors are tailored on $\alpha \text{−}{\mathrm{FeSi}}_2$ (111) thin films, while the bulk material of $\alpha \text{−}{\mathrm{FeSi}}_2$ is metallic and nonmagnetic. The transport property of the films renders two different conducting states with a strong crossover at 50 K, which is accompanied by the onset of a ferromagnetic transition as well as a substantial magnetoresistance. These experimental results are discussed in terms of the unusual electronic structure of $\alpha \text{−}{\mathrm{FeSi}}_2$ obtained within density functional calculations and Boltzmann transport calculations with and without strain. Our finding sheds light on achieving ferromagnetic semiconductors through both their structure and doping tailoring, and provides an example of a tailored material with rich functionalities for both basic research and practical applications.

We discuss an Ising spin glass where each $S=1/2$ spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte Carlo simulations to study dynamic scaling at the quantum glass transition. Comparing the dynamic exponent and other critical exponents with those of the classical (temperature-driven) transition, we conclude that quantum annealing is less efficient than classical simulated annealing in bringing the system into the glass phase. Quantum computing based on the quantum annealing paradigm is therefore inferior to classical simulated annealing for this class of problems. We also comment on previous simulations where a parameter is changed with the simulation time, which is very different from the true Hamiltonian dynamics simulated here.

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic $XXZ$ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its $q$-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young’s lattice.

We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly ramped time-dependent coin flip operation and thereby demonstrate two periodic revivals of the walker distribution. In our beam-displacer interferometer, the walk corresponds to movement between discretely separated transverse modes of the field serving as lattice sites, and the time-dependent coin flip is effected by implementing a different angle between the optical axis of half-wave plate and the light propagation at each step. Each of the quantum-walk steps required to realize a revival comprises two sequential orthogonal coin-flip operators, with one coin having constant bias and the other coin having a time-dependent ramped coin bias, followed by a conditional translation of the walker.

We present an uncertainty-relation-type quantum benchmark for continuous-variable (CV) quantum channels that works with an input ensemble of Gaussian-distributed coherent states and homodyne measurements. It determines an optimal trade-off relation between canonical quadrature noises that is unbeatable by entanglement breaking channels and refines the notion of two quantum duties introduced in the original papers of CV quantum teleportation. This benchmark can verify the quantum-domain performance for all one-mode Gaussian channels. We also address the case of stochastic channels and the effect of asymmetric gains.

We study binary spinning black holes to display the long term individual spin dynamics. We perform a full numerical simulation starting at an initial proper separation of $d\approx 25M$ between equal mass holes and evolve them down to merger for nearly 48 orbits, 3 precession cycles, and half of a flip-flop cycle. The simulation lasts for $t=20000M$ and displays a total change in the orientation of the spin of one of the black holes from an initial alignment with the orbital angular momentum to a complete antialignment after half of a flip-flop cycle. We compare this evolution with an integration of the 3.5 post-Newtonian equations of motion and spin evolution to show that this process continuously flip flops the spin during the lifetime of the binary until merger. We also provide lower order analytic expressions for the maximum flip-flop angle and frequency. We discuss the effects this dynamics may have on spin growth in accreting binaries and on the observational consequences for galactic and supermassive binary black holes.