The high-dimensional data created by high-throughput technologies require visualization
tools that reveal data structure and patterns in an intuitive form. We present PHATE, a …

The theory of quantum information, that is, of the transmission, storage, and processing of
information using quantum-mechanical systems, is now well developed. It has been …

THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that
quantum mechanics could not be a complete theory but should be supplemented by …

The unitary operators D are determined by the physical content of the theory up to a constant
factor again, which can depend on 1 and 1'. Apart from this constant however, the operations …

Polarized light is a pervasive influence in our world—and scientists and engineers in a
variety of fields require the tools to understand, measure, and apply it to their advantage …

This classic textbook by two mathematicians from the USSR's prestigious Kharkov
Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the …

The transactional interpretation of quantum mechanics (TI) is summarized and various
points concerning the TI and its relation to the Copenhagen interpretation (CI) are …

Our problems are about α the correspondence a←→ a between physical quantities a and
quantum operators a (quantization) and β the possibility of understanding the statistical …

The dependence of macroscopic systems upon their environment is studied under the
assumption that quantum theory is universally valid. In particular scattering of photons and …

The spaces with which we shall deal in this paper are Banach spaces, that is, linear, metric,
complete, normed spaces, which possess in addition a certain property of convexity of the …