Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach

TL;DR

This paper investigates the relationship between operator entanglement and Schmidt number in two-qubit unitary operations, establishing a classification and exact relations that enhance understanding of quantum entanglement measures.

Contribution

It introduces a classification of two-qubit unitary operators based on Schmidt number and clarifies the exact relation between operator entanglement and unitary parameters.

Findings

Operator entanglement is classified by Schmidt number.

Exact relations between entanglement and unitary parameters are derived.

Schmidt number serves as a key attribute linking entanglement measures.

Abstract

Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the entanglement measure of two-qubit unitary operators is classified by the Schmidt number of the unitary operators. The exact relation between the operator entanglement and the parameters of the unitary operator is clarified too.