Positive operator measure associated with homodyne tomography using the generalized Wigner function

Abstract

Recent studies have found a positive operator measure associated with quantum homodyne tomography which, with the state of a system, leads to the probability distribution p_ht^T. Here, we introduce the general integral kernel for the state T, which arises from considering the General Wigner function, and show that p_ht^T can still be expressed by the matrix elements of T when the general integral kernel is used, giving the same results as the standard integral kernel.