Multipartite entangling power by von Neumann entropy
Abstract
Quantifying the entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We introduce the definition of multipartite entangling, assisted entangling, and disentangling power, which is a natural generalization of the bipartite ones. We show that they are assumed at a specified quantum state. We analytically derive the entangling power of Schmidt-rank-two multi-qubit unitary operations by the minimal convex sum of modulo-one complex numbers. Besides we show the necessary and sufficient condition that the assisted entangling power of Schmidt-rank-two unitary operations reaches the maximum. We further investigate the widely-used multi-qubit gates, for example, the entangling and assisted entangling power of the -qubit Toffoli gate is one ebit. The entangling power of the three-qubit Fredkin gate is two ebits, and that of the four-qubit Fredkin gate is in two to ebits.
Cite
@article{arxiv.2410.15253,
title = {Multipartite entangling power by von Neumann entropy},
author = {Xinyu Qiu and Zhiwei Song and Lin Chen},
journal= {arXiv preprint arXiv:2410.15253},
year = {2024}
}