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arXiv · 2410.15253

Multipartite entangling power by von Neumann entropy

Xinyu Qiu·Zhiwei Song·Lin Chen
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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 $n$-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 $\log_25$ ebits.

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Xinyu Qiu, Zhiwei Song, Lin Chen. 2024-10-20. Multipartite entangling power by von Neumann entropy. https://doi.org/10.1103/physreva.111.022407

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