  It has been shown that the entanglement between the system state and the
ancillary state is not a strict requirement for performing ancilla-assisted
process tomography(AAPT). Instead, it only requires that the system-ancilla
state be faithful, which, in practice, is the invertibility of a certain matrix
representing the state. Our paper takes on the operational definition of
faithfulness, i.e., a state is faithful if one can extract complete information
about the quantum process, and we restrict the process to single-qubit
operations on a two-qubit system-ancilla state. We present a theoretical
analysis to connect the invertibility problem to the concept of Sinisterness,
which quantifies the correlation of two qubits. Using Sinisterness, we derive a
way of constructing two-qubit states that are guaranteed to be faithful in an
operational sense and estimate the bound on the average error of the process.
Our analysis agrees that the maximally entangled states provided the smallest
error amplification. Nevertheless, it maps out a numerical region where the
advantage of the entanglement starts.
