Spectral Properties of Tensor Products of Channels

We investigate spectral properties of the tensor products of two quantum channels defined on matrix algebras. This leads to the important question of when an arbitrary subalgebra can split into the tensor product of two subalgebras. We show that for two unital quantum channels $\mathcal{E}_1$ and $\mathcal{E}_2$ the multiplicative domain of $\mathcal{E}_1\otimes\mathcal{E}_2$ splits into the tensor product of the individual multiplicative domains. Consequently, we fully describe the fixed points and peripheral eigen operators of the tensor product of channels. Through a structure theorem of maximal unital proper $^*$-subalgebras (MUPSA) of a matrix algebra we provide a non-trivial upper bound of the 'multiplicative index' of a unital channel which was recently introduced. This bound gives a criteria on when a channel cannot be factored into a product of two different channels. We construct examples of channels which can not be realized as a tensor product of two channels in any way. With these techniques and results, we found some applications in quantum error correction.Comment: Proofs of Section 3 are simplified using a result of Ola Bratteli. Some references have been update

Generative feature-based design-by-constraints as a means of integration within the manufacturing industry

The article examines the development of computer aids within manufacturing industry and proposes an alternative approach to the way we design and the designer's role within manufacturing. A feature-based generative design-by-constraints approach is applied, which requires the designer to specify solutions in terms of manufacturing data, which is captured by means of an interactive simulation of machining processes, in which the constraints of equipment, materials and tools are displayed to the designer. The effect of this approach on the integration of all areas within a manufacturing environment is explored, as is the simultaneous design nature of this approach

A conceptual study of spirituality in selected writings of Emile Jaques-Dalcroze

Several authors have noted that one of Émile Jaques-Dalcroze’s aims was to dissolve the mind–body dualism, typical of Cartesianism. However, there has been little research on the spirit–body connection, as it appears in Jaques-Dalcroze’s writings. The purpose of this document analysis is to understand how a hermeneutic phenomenological model for spirituality in music education can inform our understanding of spirituality in selected writings by Jaques-Dalcroze. In the adapted model holism, balance, aesthetic experience, and movement in time, space, and with energy emerged as core concepts. This gives us a much richer understanding of the Dalcroze approach than has hitherto been available and adds to a growing narrative about the spiritual as it pertains to Jaques-Dalcroze and the approach he initiated