Measures of operator entanglement of two-qubit gates

TL;DR

This paper compares two measures of operator entanglement for two-qubit gates, revealing their equivalence for some classes and inequivalence for others, and relates linear entropy to local invariants.

Contribution

It establishes the relationship between different entanglement measures and local invariants for two-qubit gates, clarifying their applicability and limitations.

Findings

Schmidt strength and linear entropy are equivalent for Schmidt number 2 gates.

No one-to-one relation exists between the measures for Schmidt number 4 gates.

Linear entropy relates simply to local invariants of two-qubit gates.

Abstract

Two different measures of operator entanglement of two-qubit gates, namely, Schmidt strength and linear entropy, are studied. While these measures are shown to have one-to-one relation between them for Schmidt number 2 class of gates, no such relation exists for Schmidt number 4 class, implying that the measures are inequivalent in general. Further, we establish a simple relation between linear entropy and local invariants of two-qubit gates. The implication of the relation is discussed.