We propose a test of nonlocality for continuous variables using a two-mode squeezed state as the source of nonlocal correlations and a measurement scheme based on conditional homodyne detection. Both the Clauser-Horne-Shimony-Holt and the Clauser-Horne inequality are constructed from the conditional homodyne data and found to be violated for a squeezing parameter larger than $r\approx 0.48$.

Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, $B$, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the $B$ gate. Realization of the $B$ gate is illustrated with an example of charge-coupled superconducting qubits for which the $B$ gate is seen to be generated in shorter time than the CNOT gate.

Ensemble averages of the sensitivity to initial conditions $\xi \left(t\right)$ and the entropy production per unit of time of a new family of one-dimensional dissipative maps, $x_{t+1}=1-a{e}^{-1/|x_t{|}^z}(z>0)$, and of the known logisticlike maps, $x_{t+1}=1-a\left|x_t{|}^z\right(z>1)$, are numerically studied, both for strong (Lyapunov exponent ${\lambda }_1>0$) and weak (chaos threshold, i.e., ${\lambda }_1=0$) chaotic cases. In all cases we verify the following: (i) both $\langle {ln}_q\xi \rangle [{ln}_{q}x\equiv (x^{1-q}-1)/(1-q);{ln}_{1}x=\ln x]$ and $\langle S_q\rangle [S_q\equiv (1-\sum _i{p}_i^q)/(q-1);S_1=-\sum _i{p}_i\ln p_i]$ linearly increase with time for (and only for) a special value of $q$, $q_{\mathrm{s}\mathrm{e}\mathrm{n}}^{\mathrm{a}\mathrm{v}}$, and (ii) the slope of $\langle {ln}_q\xi \rangle$ and that of $\langle S_q\rangle$ coincide, thus interestingly extending the well known Pesin theorem. For strong chaos, $q_{\mathrm{s}\mathrm{e}\mathrm{n}}^{\mathrm{a}\mathrm{v}}=1$, whereas at the edge of chaos $q_{\mathrm{s}\mathrm{e}\mathrm{n}}^{\mathrm{a}\mathrm{v}}\left(z\right)<1$.

It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speedup of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a cnot (controlled not) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number.

We have performed a Bell-type test for energy-time entangled qutrits. A method of inferring the Bell violation in terms of an associated interference visibility is derived. Using this scheme we obtained a Bell value of $2.784\pm 0.023$, representing a violation of $34\sigma$ above the limit for local variables. The scheme has been developed for use at telecom wavelengths and using proven long distance quantum communication architecture to optimize the utility of this high dimensional entanglement resource.

A mixed quantum state $\rho$ shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of $\rho$ into a single shared pair of qubits having high fidelity with the maximally entangled state $|{\phi }^{+}\rangle =(|00\rangle +|11\rangle )/\sqrt{2}$. In this Letter it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for every positive integer $n$ there exists a state $\rho$ that is distillable, but, given $n$ or fewer copies of $\rho$, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.

We investigate how to concatenate different decoherence-free subspaces to realize scalable universal fault-tolerant quantum computation. Based on tunable $XXZ$ interactions, we present an architecture for scalable quantum computers which can fault-tolerantly perform universal quantum computation by manipulating only a single type of parameter. By using the concept of interaction-free subspaces, we eliminate the need to tune the couplings between logical qubits, which further reduces the technical difficulties for implementing quantum computation.

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.

We perform path sampling molecular dynamics on the pressure-induced reconstructive phase transition from NaCl to CsCl type structure. Unlike the molecular dynamics simulations prior to this work our approach does not drive the process by applying elevated pressure. As a consequence, we are able to observe nucleation events that initiate the successive transformation of the crystal. The competing phases are separated by an interface exhibiting a well-defined structure that propagates through the crystal during phase transition.

We analyze the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and noncoagulating phases. We show that the phase transition is related to a Kramers problem, and we use this to determine the phase diagram in two dimensions, as a function of the dimensionless inertia of the particles, $ϵ$, and a measure of the relative intensities of potential and solenoidal components of the velocity field, $\Gamma$. We find that the phase line is described by a function which is nonanalytic at $ϵ=0$, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realizations of this phase transition.

We construct a Bell inequality for coincidence probabilities on a three three-dimensional (qutrit) system. We show that this inequality is violated when each observer measures two noncommuting observables, defined by the so-called unbiased six-port beam splitter, on a maximally entangled state of two qutrits. The strength of the violation agrees with the numerical results presented by Kaszlikowski et al. , quant-ph/0202019. It is proven that the inequality defines facets of the polytope of local variable models.

We present a numerical study of classical particles diffusing on a solid surface. The particles’ motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

The effect of time-varying electromagnetic fields on electron coherence is investigated. A sinusoidal electromagnetic field produces a time-varying Aharonov-Bohm phase. In a measurement of the interference pattern which averages over this phase, the effect is a loss of contrast. This is effectively a form of decoherence. We calculate the magnitude of this effect for various electromagnetic field configurations. The result seems to be sufficiently large to be observable.

We derive the phase diagram for ultracold trapped dipolar Fermi gases. Below the critical value of the dipole-dipole interaction energy, the BCS transition into a superfluid phase ceases to exist. The critical dipole strength is obtained as a function of the trap aspect ratio. Alternatively, for a given dipole strength there is a critical value of the trap anisotropy for the BCS state to appear. The order parameter exhibits a novel nonmonotonic behavior at the criticality.

We present exact results in the Thomas-Fermi regime for the statics and dynamics of a harmonically trapped Bose-Einstein condensate that has dipole-dipole interactions in addition to the usual $s$-wave contact interactions. Remarkably, despite the nonlocal and anisotropic nature of the dipolar interactions, the density profile in a general time-dependent harmonic trap is an inverted parabola. The evolution of the condensate radii is governed by local, ordinary differential equations, and as an example we calculate the monopole and quadrupole shape oscillation frequencies.

Finding the mean of the total number $N_{\mathrm{tot}}$ of stationary points for $N$-dimensional random energy landscapes is reduced to averaging the absolute value of the characteristic polynomial of the corresponding Hessian. For any finite $N$ we provide the exact solution to the problem for a class of landscapes corresponding to the “toy model” of manifolds in a random environment. For $N\gg 1$ our asymptotic analysis reveals a phase transition at some critical value ${\mu }_c$ of a control parameter $\mu$ from a phase with a finite landscape complexity: $N_{\mathrm{tot}}\sim e^{N\Sigma }$, $\Sigma (\mu <{\mu }_c)>0$ to the phase with vanishing complexity: $\Sigma (\mu >{\mu }_c)=0$. Finally, we discuss a method of dealing with the modulus of the spectral determinant applicable to a broad class of problems.

We report evidence of coexisting period stochastic resonance (PSR) and coherence resonance (CR) phenomena in an electrochemical cell. The anodic voltage ($V$) in the cell is chosen such that the anodic current ($I$) exhibits excitable fixed point behavior. Subsequently, the anodic voltage is modulated by an external perturbation that is a composite of a subthreshold periodic pulse signal and Gaussian white noise (GWN). As the amplitude of the GWN is increased, the regularity of the invoked dynamics is analyzed using normalized variance curve. The calculated resonance curve shows a double minima, implying the existence of two optimum noise levels where enhanced regularity of the induced spike sequence is detected. Numerical simulations corroborate experimental findings.

The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.

We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS–Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-$T_c$ and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.

We have remeasured the absolute $1S$-$2S$ transition frequency ${\nu }_{\mathrm{H}}$ in atomic hydrogen. A comparison with the result of the previous measurement performed in 1999 sets a limit of $(-29\pm 57)\mathrm{Hz}$ for the drift of ${\nu }_{\mathrm{H}}$ with respect to the ground state hyperfine splitting ${\nu }_{\mathrm{Cs}}$ in ${}^{133}\mathrm{Cs}$. Combining this result with the recently published optical transition frequency in ${}^{199}\mathrm{Hg}^{+}$ against ${\nu }_{\mathrm{Cs}}$ and a microwave ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ clock comparison, we deduce separate limits on $\dot{\alpha }/\alpha =(-0.9\pm 2.9)\times {10}^{-15}{\mathrm{yr}}^{-1}$ and the fractional time variation of the ratio of Rb and Cs nuclear magnetic moments ${\mu }_{\mathrm{Rb}}/{\mu }_{\mathrm{Cs}}$ equal to $(-0.5\pm 1.7)\times {10}^{-15}{\mathrm{yr}}^{-1}$. The latter provides information on the temporal behavior of the constant of strong interaction.