Optimal Simulation of a Perfect Entangler

TL;DR

This paper derives an analytical formula for the minimum number of applications of a two-qubit entangling unitary needed to simulate a perfect entangler, revealing the entanglement strength of such operations.

Contribution

It provides a complete analytical solution to the problem of simulating perfect entanglers using a given two-qubit unitary and one-qubit unitaries as resources.

Findings

Derived an explicit formula for the optimal number of runs

Revealed the entanglement strength of two-qubit unitaries

Solved a fundamental problem in quantum entanglement simulation

Abstract

A $2\otimes 2$ unitary operation is called a perfect entangler if it can generate a maximally entangled state from some unentangled input. We study the following question: How many runs of a given two-qubit entangling unitary operation is required to simulate some perfect entangler with one-qubit unitary operations as free resources? We completely solve this problem by presenting an analytical formula for the optimal number of runs of the entangling operation. Our result reveals an entanglement strength of two-qubit unitary operations.