Finite dimensional quantum mechanics via finite geometry - Michael Revzen

Introductory approach to finite affine plane geometry is given. The geometry is used to transcribe Hilbert space entities (operators and states) to c-number functions in phase space. Mutually unbiased bases are introduced and their relation to the finite geometrical approach to underscored. Illustrative examples formulated in detail are finite dimensional Wigner function and Radon transform in phase space. The geometrical interpretation for a maximally entangled states case is outlined.