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arXiv:1007.4179 · Physical Review A

Multipartite entanglement in quantum algorithms

Dagmar Bruß, Chiara Macchiavello

Published May 17, 2011• 94 citations
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Abstract

We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyze the multipartite entanglement properties in the Deutsch-Jozsa, Grover, and Simon algorithms. Our results show that for these algorithms most instances involve multipartite entanglement.
DOI
10.1103/physreva.83.052313

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We firstly investigate the multipartite entanglement features of the quantum states, including the iteration states achieved by repeated application of Grover iteration and the Oracle ones into which the above iteration states evolve by applying single Oracle operation, employed in Grover's search algorithm by means of the separable degree and the entanglement measure. Then we give the quantitative and qualitative descriptions of the entanglement dynamics in Grover's search algorithm. Our results show that for most instances (i) the separable degrees of these states and ranges of their maximum Schmidt numbers are invariable by following the dynamics of Grover's search algorithm; (ii) the dynamics of Grover's search algorithm is almost "filled" by the fully entangled states.
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Quantum entanglement, a fundamental aspect of quantum mechanics, has captured significant attention in the era of quantum information science. In multipartite quantum systems, entanglement plays a crucial role in facilitating various quantum information processing tasks, such as quantum teleportation and dense coding. In this article, we review the theory of multipartite entanglement measures, with a particular focus on the genuine as well as the operational meaning of multipartite entanglement measures. By providing a thorough and valuable insight on this field, we hope that this review would inspire and guide researchers in their endeavors to further develop novel approaches for characterizing multipartite entanglement.