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Homological Analysis of Multi-Qubit Entanglement
Alessandra di Pierro, Stefano Mancini, Laleh Memarzadeh, Riccardo Mengoni
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.