Volume 123, Number 3, August 2018
|Number of page(s)||7|
|Published online||04 September 2018|
Homological analysis of multi-qubit entanglement
1 Department of Informatics, University of Verona - Strada Le Grazie 15, 37134 Verona, Italy
2 School of Science and Technology, University of Camerino - 62032 Camerino, Italy
3 INFN, Sezione di Perugia - Via A. Pascoli, 06123 Perugia, Italy
4 Department of Physics, Sharif University of Technology - Teheran, Iran
Received: 13 February 2018
Accepted: 7 August 2018
We propose the usage of persistent homologies to characterize multipartite entanglement. On a multi-qubit data set we introduce metric-like measures defined in terms of bipartite entanglement and then we derive barcodes. We show that, depending on the distance, they are able to produce different classifications. In one case, it is possible to obtain the standard separability classes. In the other case, a new classification of entangled states of three and four qubits is provided.
PACS: 03.67.Mn – Entanglement measures, witnesses, and other characterizations / 02.40.Re – Algebraic topology / 02.70.-c – Computational techniques; simulations
© EPLA, 2018
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