A short history of frames and quantum designs
Bernhard Bodmann, John Haas
TL;DR
This survey explores the relationship between frame theory and quantum information, emphasizing quantum 2-designs as optimal arrangements for quantum state tomography and collecting known examples.
Contribution
It provides a comprehensive overview of quantum 2-designs, highlighting their significance in quantum state tomography and compiling existing examples in the field.
Findings
Quantum 2-designs are optimal for quantum state tomography.
The survey links frame theory with quantum measurement strategies.
Most known quantum 2-design examples are compiled in the paper.
Abstract
In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense optimal for quantum state tomography. After a brief introduction, we discuss the role of POVMs in quantum theory, developing the importance of quantum 2-designs. In the final section, we collect many if not most known examples of quantum-2 designs to date.
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