Multipartite entangling power by von Neumann entropy

• URL: http://arxiv.org/abs/2410.15253v1
• Date: Sun, 20 Oct 2024 02:18:36 GMT
• Title: Multipartite entangling power by von Neumann entropy
• Authors: Xinyu Qiu, Zhiwei Song, Lin Chen,
• Abstract summary: Quantifying entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We analytically derive the entangling power of Schmidt-rank-two multi-qubit unitary operations by the minimal convex sum of modulo-one complex numbers. We investigate the widely-used multi-qubit gates, for example, the entangling and assisted entangling power of the $n$-qubit Toffoli gate is one ebit.
• Score: 6.193378336510727
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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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