Ancilla-Assisted Process Tomography with Bipartiete Mixed Separable States

Abstract: It has been shown that the entanglement between the system and ancillary states is not a strict requirement for performing ancilla-assisted process tomography(AAPT). Instead, from a theoretical point of view, it only requires that the system-ancilla state be faithful, which, in the qubit case, 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 that connects the invertibility problem to the concept of Sinisterness, which quantifies the correlation between two qubits and can be generalized to bipartite systems formed by qubits for a certain class of states. Using Sinisterness, we derive a way of constructing two-qubit states that are guaranteed to be faithful and estimate the bound on the average error of the process featured by the condition number. 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.