By means of a $\mathrm{mod}\left(N\right)$-invariant operator basis, $s$-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and their properties are discussed in details. The discrete Glauber-Sudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of $s$-parametrized phase-space functions where, in particular, a hierarchical process among them is promptly established. In addition, a phase-space description of quantum tomography and quantum teleportation is presented and new results are obtained.

• Received 13 April 2005

DOI:https://doi.org/10.1103/PhysRevA.72.042308