On discrete structures in finite Hilbert spaces
Abstract
We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function, symmetric informationally complete measurements, projective and unitary tdesigns are discussed. Some recent results in the field are covered and several important open questions are formulated. We advocate a geometric approach to the subject and emphasize numerous links to various mathematical problems.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.07902
 arXiv:
 arXiv:1701.07902
 Bibcode:
 2017arXiv170107902B
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 30 pages with 5 figures. Preprint based on a new chapter written to the second edition of the book "Geometry of Quantum States. An introduction to Quantum Entanglement", CUP, Cambridge, to appear in 2017