Complete hierarchy of linear systems for certifying quantum entanglement of subspaces

Nathaniel Johnston, Benjamin Lovitz, Aravindan Vijayaraghavan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in the sense that every entangled subspace is shown to be so at some finite level of the hierarchy. It straightforwardly generalizes to the case of higher Schmidt rank, as well as the multipartite cases of completely and genuinely entangled subspaces. These hierarchies work extremely well in practice even in very large quantum systems, as they can be implemented via elementary linear algebra techniques rather than the semidefinite programming techniques that are required by previously known hierarchies.

Original languageEnglish (US)
Article number062443
JournalPhysical Review A
Issue number6
StatePublished - Dec 2022

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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