Designing tight frames for quantum computing
Source: Originally published on arXiv quant-ph on July 31, 2026.
arXiv:2607.27247v1 Announce Type: new Abstract: The aim of this thesis is to explore the implementation of a special kind of quantum measurements, so called harmonic tight frames. To achieve this goal, representation theory is addressed, emphasizing its construction from irreducible representations and the relations they satisfy. These tools simplify the study due to the existence of symmetries, leading to the concept of group frames, defined as orbits under the unitary action of a group and characterized by their symmetry groups. Among the various groups, the simplest are the abelian ones, giving rise to harmonic frames, which are analyzed through the classification theorem of abelian groups and the characters of their irreducible representations. In the quantum mechanics context, the fra...
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