We propose an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by unitary processing of the probe beams and coherent feedback to the register qubits. We exploit a limit theorem for quantum stochastic differential equations to analyze coherent feedback networks based on the bit-flip/phase-flip code, obtaining simple closed-loop master equations with only four Hilbert-space dimensions required for the controller. Our approach is well matched to physical implementations that feature solid-state qubits embedded in planar electromagnetic circuits.

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schr\"odinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.

Electromagnetic negative refraction in metamaterials has attracted increasingly great interest, since its first experimental verification in 2001. It potentially leads to the applications superior to conventional devices including compact antennas for mobile stations, imaging beyond the diffraction limit, and high-resolution radars, not to mention the anamolous wave propagation in fundamental optics. Here, we report how metamaterials could be used to simulate the "negative refraction of spin-zero particles interacting with a strong potential barrier", which gives rise to the Klein paradox--a counterintuitive relativistic process. We address the underlying physics of analogous wave propagation behaviours in those two entirely different domains of quantum and classical.

We constructed a cavity QED system with a diamagnetic atom of 171Yb and performed projective measurements on a single nuclear spin. Since Yb has no electronic spin in its ground state, a significantly longer coherence time is expected compared with the paramagnetic atoms. Since the nuclear spin of 171Yb is 1/2, the procedure of spin polarization and state verification can be dramatically simplified compared with the pseudo spin-1/2 system. By enhancing the photon emission rate of 1S0-3P1 transition, we verify the nuclear spin state of an atom with the measurement time of T_meas=30us and S/N=10^2. This performance for the single nuclear spin measurement will enable the available number of atomic qubits in quantum information processing to be increased.

One of the most important problems in Physics is how to reconcile Quantum Mechanics with General Relativity. Some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favor of a more general theory. However, as the experiments we can perform nowadays are far away from the range of energies where we may expect to observe non-quantum effects, it is difficult to theorize at this respect. Here we propose a fundamental axiom that we believe any reasonable post-quantum theory should satisfy, namely, that such a theory should recover classical physics in the macroscopic limit. We use this principle, together with the impossibility of instantaneous communication, to characterize the set of correlations that can arise between two distant observers. Although several quantum limits are recovered, our results suggest that quantum mechanics could be falsified by a Bell-type experiment if both observers have a sufficient number of detectors.

We consider two systems of harmonically trapped particles in a typical pure state of the Hilbert space defined by given values of the particle numbers and energies of the two gases. Such a state is entangled but we show that, for large systems, the resulting correlations between the two gases are identical to those of a separable mixture. This result can be generalized to other physical systems. We discuss the relation of this effective separability to the well-known existence of quantum correlations in any entangled state. We study in detail a small bipartite system and find that its correlations are well explained by the large systems results.

We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer for a subspace is defined as the group of Pauli operators whose eigenvalues are +1 on the subspace. The group can be generated by a subset of operators in the stabilizer, and the choice of generators determines the structure of the graph. The Wolff algorithm, together with the histogram method and finite-size scaling, is used to calculate both the critical temperature and the critical exponents of each structure. The simulations show that the choice of stabilizer generators, both the number and the geometry, has a large effect on the critical temperature.

We propose a quantum optical interface between an atomic and solid state system. We show that quantum states in a single trapped atom can be entangled with the states of a semiconductor quantum dot through their common interaction with a classical laser field. The interference and detection of the resulting scattered photons can then herald the entanglement of the disparate atomic and solid-state quantum bits. We develop a protocol that can succeed despite a significant mismatch in the radiative characteristics of the two matter-based qubits. We study in detail a particular case of this interface applied to a single trapped \Yb ion and a cavity-coupled InGaAs semiconductor quantum dot. Entanglement fidelity and success rates are found to be robust to a broad range of experimental nonideal effects such as dispersion mismatch, atom recoil, and multi-photon scattering. We conclude that it should be possible to produce highly entangled states of these complementary qubit systems under realistic experimental conditions.

A central question in qubit decoherence is the extent to which the characteristics of the noise can be backed out from qubit measurements. This is particularly important for 1/f and other types of broad-spectrum noise. For certain types of qubits, the working point (the angle between the energy axis and the noise coupling axis) can be varied. Using a new mathematical method that is suited to treat all angles, we present theoretical results that show how this degree of freedom can be used to extract noise parameters and to identify when the topology of the Bloch sphere is important. The basic idea is that changing the working point can change the noise sources from weak to strong coupling, and that the effects of the two different kinds of sources are qualitatively different. This technique can be used to produce looping on the Bloch sphere.

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.

When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on the two-dimensional Heisenberg model on a depleted square lattice, where fidelity estimators show marked behaviours at two successive quantum phase transitions.