Reconstructing the discrete Wigner function and some properties of the measurement bases -: art. no. 012106

We derive a direct reconstruction algorithm for the discrete Wigner function through different types of measurements. For a system described in a Hilbert space of dimension N=N-1...N-p, where the numbers N-i are prime, the reconstruction is accomplished with (N-1+1)...(N-p+1) factorable (local) von Neumann measurements. For the special case where the dimension is a power of a prime, the reconstruction can be performed in a much more efficient way using N+1 complementary measurements. If the system is composed of a number of smaller subsystems, these measurements will then in general be nonseparable.