Quantum information theory has developed dramatically over the past decade, driven by the prospects of quantum-enhanced communication and computation systems. Among the most striking successes, one finds for example the discovery of quantum factoring, quantum key distribution, or quantum teleportation. Most of these concepts were initially developed for discrete quantum variables, in particular...

Davis 1] has investigated the properties of the Waltz propagation algorithm with interval labels in continuous domains. He shows that in most cases, the algorithm does not achieve arc consistency, and furthermore is subject to innnite iterations. In this paper, I show that the main reason for Davis' negative results lies in the way he formulates the propagation rule for the Waltz algorithm. For...

Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes them from discrete random variables, which can take on only a sequence of values, usually integers. Typically random variables that represent, for example, time or distance will be continuous rather than discrete. Just as we descri...

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fi...

Quantum teleportation is analyzed for states of dynamical variables with continuous spectra, in contrast to previous work with discrete (spin) variables. The entanglement fidelity of the scheme is computed, including the roles of finite quantum correlation and nonideal detection efficiency. A protocol is presented for teleporting the wave function of a single mode of the electromagnetic field w...

A scheme to achieve dense quantum coding for the quadrature amplitudes of the electromagnetic field is presented. The protocol utilizes shared entanglement provided by nondegenerate parametric down-conversion in the limit of large gain to attain high efficiency. For a constraint in the mean number of photons n̄ associated with modulation in the signal channel, the channel capacity for dense codi...

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. This article reviews the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations...

This paper considers structural optimization problems featuring discrete variables, as well as nonlinear implicit constraints which can only be evaluated through time-expensive computations. A prominent application consists in the preliminary structural design of large ships, where many of the variables take their values in discrete sets which model standard element dimensions to be selected fr...