On discrete structures in finite Hilbert spaces

Understand

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 t--designs 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.