Unbiased nonorthogonal bases for tomographic reconstruction

Abstract

We have developed a general method for constructing a set of nonorthogonal bases with equal separations between all different basis states in prime dimensions. The results are that the corresponding biorthogonal counterparts are pairwise unbiased with the components of the original bases. Using these bases, we derive an explicit expression for the optimal tomography in nonorthogonal bases. A special two-dimensional case is analyzed separately.