Nonlocal characteristics of two-qubit gates and their argand diagrams

Abstract: In this paper, we show the usefulness of the chords present in the argand diagram of squared eigenvalues of nonlocal part of two-qubit gates to study their nonlocal characteristics. We discuss the criteria for perfect entanglers to transform a pair of orthonormal product states into a pair of orthonormal maximally entangled states. Perfect entanglers with a chord passing through origin can do such a transformation. In the Weyl chamber, we identify the regions of perfect entanglers with at least one chord passing through origin. We also provide the conditions for a perfect entangler without any chord passing through origin to transform a pair of orthonormal product states into orthonormal maximally entangled states. Finally, we show that similar to entangling power, gate typicality can also be described using the chords present in the argand diagram. For each chord describing the entangling power, there exists a chord describing the gate typicality. We show the geometrical relation between the two sets of chords.