Abstract:
We examine bipartite and multipartite correlations within the construct of unitary orbits. We show that the set of product states is a very small subset of set of all possible states, while all unitary orbits contain classically correlated states. Using this we give meaning to degeneration of quantum correlations due to a unitary interactions, which we call coherent correlations. The remaining classical correlations are called incoherent correlations and quantified in terms of the distance of the joint probability distributions to its marginals. Finally, we look at how entanglement looks in this picture for the two-qubit case.

Abstract:
We characterize the set of ground states that can be synthesized by classical 2-body Ising Hamiltonians. We then construct simple Ising planar blocks that simulates efficiently a universal set of logic gates and connections, and hence any boolean function. We therefore provide a new method of encoding universal computation in the ground states of Ising lattices, and a simpler alternative demonstration of the known fact that finding the ground state of a finite Ising spin glass model is NP complete. We relate this with our previous result about emergence properties in infinite lattices.

Abstract:
A quantum password is a quantum mechanical analogue of the classical password. Our proposal is completely quantum mechanical in nature, i.e. at no point is information stored and manipulated classically. We show that, in contrast to quantum protocols that encode classical information, we are able to prevent the distribution of reusable passwords even when Alice actively cooperates with Eve. This allows us to confront and address security issues that are unavoidable in classical protocols.

Abstract:
The relationship between efficient quantum gate synthesis and control theory has been a topic of interest in the quantum control literature. Motivated by this work, we describe in the present article how the dynamic programming technique from optimal control may be used for the optimal synthesis of quantum circuits. We demonstrate simulation results on an example system on SU(2), to obtain plots related to the gate complexity and sample paths for different logic gates.

Abstract:
We explicitly compute the optimal cost for a class of example problems in geometric quantum control. These problems are defined by a Cartan decomposition of $su(2^n)$ into orthogonal subspaces $\mathfrak{l}$ and $\mathfrak{p}$ such that $[\mathfrak{l},\mathfrak{l}] \subseteq \mathfrak{p}, [\mathfrak{p},\mathfrak{l}] = \mathfrak{p}, [\mathfrak{p},\mathfrak{p}] \subseteq \mathfrak{l}$. Motion in the $\mathfrak{l}$ direction are assumed to have negligible cost, where motion in the $\mathfrak{p}$ direction do not. In the special case of two qubits, our results correspond to the minimal interaction cost of a given unitary.

Abstract:
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. We show that for any Gaussian cluster state, the canonical generation scheme in terms of QND-type interactions, can be entirely replaced by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful and we propose a systematic way to create cheaper states. As an application, we consider Gaussian cluster computation in multiple-rail encoding. This encoding may reduce errors due to finite squeezing, even when the extra rails are achieved through off-line squeezing and linear optics.

Abstract:
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the amount of resources needed to forecasting a system's behaviour. Another one (the effective measure complexity, aka excess entropy) is a measure of mutual information stored in the system proper. We show that for any given system the two measures differ by the amount of information erased during forecasting. We interpret the difference as inefficiency of a given model. We find a bound to the ratio of the two measures defined as information-processing efficiency, in analogy to the second law of thermodynamics. This new link between two prominent measures of complexity provides a quantitative criterion for good models of complex systems, namely those with little information erasure.

Abstract:
In 1972, P.W.Anderson suggested that `More is Different', meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such systems, and indicates that even if a `theory of everything' governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights.

Abstract:
Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of Occam's razor, simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. We systematically construct quantum models that break this classical bound, and show that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved.

Abstract:
We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity QED parameters and with nonideal coupling.