/******************************************************************************
  We define a Hermitian operator ProjTo0 which is a projector to |0> basis
  vector. If it is given a maximally mixed state, it renormalizes the state.
 ******************************************************************************/
hermitian ProjTo0 = [
    [sqrt(2), 0],
    [0,       0]];

 /******************************************************************************
  We define a Hermitian operator ProjTo1 which is a projector to |1> basis
  vector. If it is given a maximally mixed state, it renormalizes the state.
 ******************************************************************************/
hermitian ProjTo1 = [
    [0,  0      ],
    [0,  sqrt(2)]];