
Quantendesigns: Grundzüge einer nichtkommutativen Designtheorie,
Ph.D. Thesis, University of Vienna, 1999

Download (German, pdf, 77 pages, 442 KB).

Quantum Designs: Foundations of a noncommutative Design Theory,
English translation of the Ph.D. Thesis (including a new preface 2010)

Download (pdf, 79 pages, 468 KB).
Published in the International Journal of Quantum Information (IJQI), Volume 9, Issue 1, February 2011, page 445507.
[DOI No: 10.1142/S0219749911006776], © Copyright World Scientific Publishing Company,
see IJQI.
The thesis contains an overall presentation of quantum designs, based on the terminology
given here.
A list of Citations (external link).

Orthogonale Lateinische Quadrate und Anordnungen, Verallgemeinerte HadamardMatrizen und
Unabhängigkeit in der QuantenWahrscheinlichkeitstheorie,
Master (Diploma) Thesis, University of Vienna, 1991 
Download (German, pdf, 87 pages, 7273 KB)
This paper contains a presentation and analysis of the concept of independent observables 
a generalization of affine designs. The spectral decomposition
of k selfadjoint matrices A_{1}, ..., A_{k} defines k
complete orthogonal classes on the quantum design built up from all the projections. The orthogonal
classes, resp. obervables, A_{i} are said to be mutually independent
(w.r.t. the density matrix (1/d)I), if
.
For regular quantum design this reduced to the definition of affine designs, and with the case r=1
to MUBs. This definition also covers the (basic) mutually independence of
A_{i} = B_{i} I and
A_{j} = I B_{j} for any
selfadjoint matrices B_{i}, B_{j}.
This definition also allows a generalization to infinite dimensional Hilbert Spaces: Let A
and B be two selfadjoint operators over a seperable HilbertSpace with spectrum
respectively. Let further be the characteristic
functions of Borel subsets E, F of the spectrum of A and B, hence
be spectral projections of A and B.
We say that A and B are independent if there are Borel
measures on the spectrum of A and B such,
that for any two compact subset
E and F the following relation holds:
Please notice, that for arbitrary projections P_{1} and P_{2}
in infinitedimensional Hilbert spaces
tr(P_{1}P_{2}P_{1}) =
tr(P_{2}P_{1}P_{2}) holds (the expression
tr(P_{1}P_{2}) is generally not defined).
It can be shown, that the position operator X
and the impuls operator P are mutually independent, as well as linearcombinations of these two.

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