SIC-POVM

A symmetric, informationally complete, positive operator valued measure (SIC-POVM) is a special case of a generalized measurement on a Hilbert space, used in the field of quantum mechanics. A measurement of the prescribed form satisfies certain defining qualities that makes it an interesting candidate for a "standard quantum measurement," utilized in the study of foundational quantum mechanics, most notably in QBism. Furthermore, it has been shown that applications exist in quantum state tomography and quantum cryptography, and a connection has been discovered with Hilbert's twelfth problem.

Due to the use of SIC-POVMs primarily in quantum mechanics, Dirac notation will be used throughout this article to represent elements in a Hilbert space.

A POVM over a ${\displaystyle d}$-dimensional Hilbert space ${\displaystyle {\mathcal {H}}}$ is a set of ${\displaystyle m}$ positive semidefinite operators ${\displaystyle \{F_{i}\}}$ on the Hilbert space that sum to the identity:

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