Document type
ArticleVersion
Accepted versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192382
Characterization of quantum entanglement via a hypercube of Segre embeddings
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
A particularly simple description of separability of quantum states arises naturally in the setting of complex algebraic geometry, via the Segre embedding. This is a map describing how to take products of projective Hilbert spaces. In this paper, we show that for pure states of $n$ particles, the corresponding Segre embedding may be described by means of a directed hypercube of dimension $(n-1)$, where all edges are bipartite-type Segre maps. Moreover, we describe the image of the original Segre map via the intersections of images of the $(n-1)$ edges whose target is the last vertex of the hypercube. This purely algebraic result is then transferred to physics. For each of the last edges of the Segre hypercube, we introduce an observable which measures geometric separability and is related to the trace of the squared reduced density matrix. As a consequence, the hypercube approach allows to measure entanglement, naturally relating bipartitions with $q$-partitions for any $q \geq 1$. We test our observables against well-known states, showing that these provide well-behaved and fine measures of entanglement.
Subject (English)
Citation
Citation
CIRICI, Joana, SALVADÓ SERRA, Jordi and TARON I ROCA, Josep. Characterization of quantum entanglement via a hypercube of Segre embeddings. Quantum Information Processing. 2021. Vol. 20. ISSN 1570-0755. [consulted: 14 of June of 2026]. Available at: https://hdl.handle.net/2445/192382