Entangling power of two-qubit unitary operations

TL;DR

This paper derives formulas for the entangling power of two-qubit unitary operations, especially when certain parameters are equal, and extends the analysis to higher-dimensional bipartite unitaries.

Contribution

It provides analytical expressions for the entangling power of specific two-qubit unitaries and generalizes the concept to bipartite unitaries of Schmidt rank two.

Findings

Analytical formulas for entangling power when c2=c3.

Explicit entangling power expressions for two example unitaries.

Extension of entangling power computation to higher-dimensional bipartite unitaries.

Abstract

The entangling power of a bipartite unitary operation shows the maximum created entanglement with the product input states. For an arbitrary two-qubit unitary operation, it is sufficient to consider its normalized operation $U$ with parameters $c_0,c_1,c_2$ and $c_3$. We show how to compute the entangling power of $U$ when $c_2=c_3$. In particular we construct the analytical expressions of entangling power of such $U$ for two examples. We also construct the entangling power of bipartite unitary operations of Schmidt rank two for any dimensions.