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arXiv:1910.09665 · Physical Review Research

Fine-structure classification of multiqubit entanglement by algebraic geometry

Masoud Gharahi, Stefano Mancini, Giorgio Ottaviani

Published Oct 1, 2020• 22 citations
arXivHTMLPDF

Abstract

The authors use algebraic-geometry tools, secant varieties, and l-multilinear ranks, to present an entanglement classification of generic n-qubit pure states under stochastic local operation and classical communication that is based on a finite number of families and subfamilies.
DOI
10.1103/physrevresearch.2.043003

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We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .