Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster-state model, and it was hence believed that with this approach, many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as “computationally universal” states—i.e., they allow one to efficiently reproduce the classical output of each quantum computation—whereas the cluster states are universal in a stronger sense since they are “universal state preparators.” Here, we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.

We show that classical many-particle systems interacting with certain soft pair interactions in two dimensions exhibit novel low-temperature behaviors. Ground states span from disordered to crystalline. At some densities, a large fraction of normal-mode frequencies vanish. Lattice ground-state configurations have more vanishing frequencies than disordered ground states at the same density and exhibit vanishing shear moduli. For the melting transition from a crystal, the thermal expansion coefficient is negative. These unusual results are attributed to the topography of the energy landscape.

We report on the experimental observation of the phase angle of a particle escaping over a periodically modulated potential barrier. Optical tweezers and back-focal plane position detection were used to record particle trajectories in the entire double-well potential. These measurements provide a sensitive test of theories proposed in the past decade of escape driven by random thermal noise from a periodically modulated potential. The observed phase shifts as a function of modulation frequency are consistent with those calculated using existing theories.

A simple expression for the conductance steps in inelastic electron tunneling from spin excitations in a single magnetic atom adsorbed on a nonmagnetic metal surface is derived. The inelastic coupling between the tunneling electron and the spin is via the exchange coupling and is treated in an impulsive approximation using the Tersoff-Hamann approximation for the tunneling between the tip and the sample.

We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension $d\ge 3$. This universality proves that, according to quantum mechanics, there are no “classical” states.

We present a pair of simultaneous conjugate Ramsey-Bordé atom interferometers using large ($20\hslash k$)-momentum transfer beam splitters, where $\hslash k$ is the photon momentum. Simultaneous operation allows for common-mode rejection of vibrational noise. This allows us to surpass the enclosed space-time area of previous interferometers with a splitting of $20\hslash k$ by a factor of 2500. Using a splitting of $10\hslash k$, we demonstrate a 3.4 ppb resolution in the measurement of the fine structure constant. Examples for applications in tests of fundamental laws of physics are given.

We analyze the non-Markovian stochastic Schrödinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of continuous quantum measurement). For the first time, we give the explicit general solution for the free particle case ($H=p^2/2m$) and discuss the main properties. We analyze the case of an exponential correlation function for the noise, giving a quantitative description of the dynamics and of its dependence on the correlation time.

The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be generated between spins, and how well an unknown state can be cloned. This situation is remedied by giving a set of sufficient conditions such that a Completely Positive map can be optimally implemented as a teleportation operation into a standard, reference, state. The case of arbitrary $1\to N$ asymmetric cloning of $d$-dimensional spins can then be solved exactly, yielding the concept of “singlet monogamy.” The utility of this relation is demonstrated by calculating properties of Heisenberg systems, and contrasting them with the results from standard monogamy arguments.

We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).

We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that $\mu$ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps $C_{\mu }$ such that the probability $\mathrm{Prob}(\mu )$ is the fidelity of each map, i.e., $\mathrm{Prob}(\mu )=\mathrm{Tr}[\rho C_{\mu }(\rho )]$. Here, the map $C_{\mu }$ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure).

We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)], a Bell-like state was generated, and three expectation values were determined. The observed violation $2.291\pm 0.008\nleqq 1$ clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.

The possibility to modify the strength of the Casimir effect by tailoring the dielectric functions of the interacting surfaces is regarded as a unique opportunity in the development of micro- and nanoelectromechanical systems. In air, however, one expects that, unless noble metals are used, the electrostatic force arising from trapped charges overcomes the Casimir attraction, leaving no room for exploitation of Casimir force engineering at ambient conditions. Here we show that, in the presence of a conductive oxide, the Casimir force can be the dominant interaction even in air, and that the use of conductive oxides allows one to reduce the Casimir force up to a factor of 2 when compared to noble metals.

Decoherence may significantly affect the polarization state of optical pulses propagating in dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the pulse. Here we report on the suppression of polarization decoherence in a ring cavity obtained by properly retooling for photonic qubits the “bang-bang” protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to quantum information processes involving flying polarization qubits.

A universal mechanism for the generation of statistical self-similarity—i.e., fractality in the context of random processes—is established. We consider a generic system which superimposes independent stochastic signals, producing a system output; all signals share a common statistical signal pattern, yet each signal has its own transmission parameters—amplitude, frequency, and initiation epoch. We characterize the class of parameter randomizations yielding statistically self-similar outputs in a universal fashion—i.e., for whatever signals fed into the system. Statistically self-similar outputs with finite variance further display (i) anomalous diffusion behavior—characterized by power-law temporal variance growth—and (ii) $1/f$ noise behavior—characterized by power-law power spectra. The mechanism presented is a “randomized central limit theorem” for fractal statistics of random processes.

A modified fluctuation-dissipation theorem for a nonequilibrium steady state is experimentally checked by studying the position fluctuations of a colloidal particle whose motion is confined in a toroidal optical trap. The nonequilibrium steady state is generated by means of a rotating laser beam which exerts on the particle a sinusoidal conservative force plus a constant nonconservative one. The modified fluctuation-dissipation theorem is perfectly verified by the experimental data. It can be interpreted as an equilibriumlike fluctuation-dissipation relation in the Lagrangian frame of the mean local velocity of the particle.

We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles nonspheroidal, nonaxisymmetric objects, and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.

Recent studies have shown that applying a sequence of Hahn spin-echo pulses to a qubit system at judiciously chosen intervals can, in certain noise environments, greatly improve the suppression of phase errors compared to traditional dynamical decoupling approaches. By enforcing a simple analytical condition, we obtain sets of dynamical decoupling sequences that are designed for optimized noise filtration, but are independent of the noise spectrum up to a single scaling factor set by the coherence time of the system. These sequences are tested in a model qubit system, ions in a Penning trap. Our combined theoretical and experimental studies show that in high-frequency-dominated noise environments with sharp high-frequency cutoffs this approach may suppress phase errors orders of magnitude more efficiently than comparable techniques can.

We study the one-dimensional Bose gas in spatially correlated disorder at zero temperature, using an extended density-phase Bogoliubov method. We analyze, in particular, the decay of the one-body density matrix and the behavior of the Bogoliubov excitations across the phase boundary. We observe that the transition to the Bose-glass phase is marked by a power-law divergence of the density of states at low energy. A measure of the localization length displays a power-law energy dependence in both regions, with the exponent equal to $-1$ at the boundary. We draw the phase diagram of the superfluid-insulator transition in the limit of small interaction strength.

We present a method, based on a non-Markovian Langevin equation, to include quantum corrections to the classical dynamics of ions in a quasiharmonic system. By properly fitting the correlation function of the noise, one can vary the fluctuations in positions and momenta as a function of the vibrational frequency, and fit them so as to reproduce the quantum-mechanical behavior, with minimal a priori knowledge of the details of the system. We discuss the application of the thermostat to diamond and to ice $\mathrm{I}h$. We find that results in agreement with path-integral methods can be obtained using only a fraction of the computational effort.

We study the effect of localized modes in lattices of size $N$ with parity-time ($\mathcal{P}\mathcal{T}$) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting $\delta \sim {exp}^{-N/\xi }$ where $\xi$ is their localization length. The level “evolution” with respect to the $\mathcal{P}\mathcal{T}$ breaking parameter $\gamma$ shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous $\mathcal{P}\mathcal{T}$ symmetry breaking occurs at ${\gamma }_{\mathcal{P}\mathcal{T}}\sim \min \{\delta \}$, thus resulting in an exponentially narrow exact $\mathcal{P}\mathcal{T}$ phase. As $N/\xi$ decreases, it becomes more robust with ${\gamma }_{\mathcal{P}\mathcal{T}}\sim 1/N^2$ and the distribution $\mathcal{P}({\gamma }_{\mathcal{P}\mathcal{T}})$ changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.