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|Title: ||Welch Bounds and Quantum State Tomography|
|Authors: ||Belovs, Aleksandrs|
|Approved Date: ||22-Dec-2008 |
|Date Submitted: ||2008 |
|Abstract: ||In this thesis we investigate complete systems of MUBs and SIC-POVMs. These are highly
symmetric sets of vectors in Hilbert space, interesting because of their applications in quantum
tomography, quantum cryptography and other areas. It is known that these objects
form complex projective 2-designs, that is, they satisfy Welch bounds for k = 2 with equality.
Using this fact, we derive a necessary and sufficient condition for a set of vectors to be
a complete system of MUBs or a SIC-POVM. This condition uses the orthonormality of a
specific set of vectors.
Then we define homogeneous systems, as a special case of systems of vectors for which
the condition takes an especially elegant form. We show how known results and some new
results naturally follow from this construction.|
|Program: ||Combinatorics and Optimization|
|Department: ||Combinatorics and Optimization|
|Degree: ||Master of Mathematics|
|Appears in Collections:||Electronic Theses and Dissertations (UW)|
Faculty of Mathematics Theses and Dissertations
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