Relations for classical communication capacity and entanglement capability of two-qubit operations

Bipartite operations underpin both classical communication and entanglement generation. Using a superposition of classical messages, we show that the capacity of a two-qubit operation for error-free entanglement-assisted bidirectional classical communication can not exceed twice the entanglement capability. In addition we show that any bipartite two-qubit operation can increase the communication that may be performed using an ensemble by twice the entanglement capability.Comment: 4 page

Quantum Graphical Models and Belief Propagation

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.Comment: 58 pages, 9 figure

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture

Entangling power and operator entanglement in qudit systems

We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimensional qudits is proportional to the corresponding operator entanglement if linear entropy is adopted as the quantity representing the degree of entanglement. We discuss the entangling power and operator entanglement of three representative quantum gates on qudits: the SUM, double SUM, and SWAP gates.Comment: 8 pages, 1 figure. Version 3: Figure was improved and the MS was a bit shortene

Entanglement capability of self-inverse Hamiltonian evolution

We determine the entanglement capability of self-inverse Hamiltonian evolution, which reduces to the known result for Ising Hamiltonian, and identify optimal input states for yielding the maximal entanglement rate. We introduce the concept of the operator entanglement rate, and find that the maximal operator entanglement rate gives a lower bound on the entanglement capability of a general Hamiltonian.Comment: 4 pages, no figures. Version 3: small change

Einstein, incompleteness, and the epistemic view of quantum states

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. Indeed, representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell's theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein's preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein's attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927.Comment: 18 pages, 8 figures, 1 recipe for cupcakes; comments welcom

Microstructural evolution of Au/TiO2 nanocomposite films: The influence of Au concentration and thermal annealing

Nanocomposite thin films consisting of a dielectric matrix, such as titanium oxide (TiO2), with embedded gold (Au) nanoparticles were prepared and will be analysed and discussed in detail in the present work. The evolution of morphological and structural features was studied for a wide range of Au concentrations and for annealing treatments in air, for temperatures ranging from 200 to 800 °C. Major findings revealed that for low Au atomic concentrations (at.%), there are only traces of clustering, and just for relatively high annealing temperatures, T ≥ 500 °C. Furthermore, the number of Au nanoparticles is extremely low, even for the highest annealing temperature, T = 800 °C. It is noteworthy that the TiO2 matrix also crystallizes in the anatase phase for annealing temperatures above 300 °C. For intermediate Au contents (5 at.% ≤ CAu ≤ 15 at.%), the formation of gold nanoclusters was much more evident, beginning at lower annealing temperatures (T ≥ 200 °C) with sizes ranging from 2 to 25 nm as the temperature increased. A change in the matrix crystallization from anatase to rutile was also observed in this intermediate range of compositions. For the highest Au concentrations (> 20 at.%), the films tended to form relatively larger clusters, with sizes above 20 nm (for T ≥ 400 °C). It is demonstrated that the structural and morphological characteristics of the films are strongly affected by the annealing temperature, as well as by the particular amounts, size and distribution of the Au nanoparticles dispersed in the TiO2 matrix.This research is sponsored by FEDER funds through the programme COMPETE – Programa Operacional Factores de Competitividade – and by national funds through FCT – Fundação para a Ciência e a Tecnologia –, under the projects PEST-C/FIS/UI607/2013 and PEst-C/EME/UI0285/2013. The authors also acknowledge the financial support by the European Project Nano4Color — Design and develop a new generation of color PVD coatings for decorative applications (FP7 EC R4SME Project No. 315286)

ASEAN and interconnecting regional spheres: Lessons for the Indian Ocean Region

10.1080/19480881.2012.683628Journal of the Indian Ocean Region8154-7