Can entanglement hide behind triangle-free graphs?

• URL: http://arxiv.org/abs/2010.11891v3
• Date: Mon, 29 Mar 2021 15:03:07 GMT
• Title: Can entanglement hide behind triangle-free graphs?
• Authors: Satvik Singh
• Abstract summary: We show that diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. We also develop a recipe to construct a plethora of unique classes of positive partial transpose entangled triangle-free states in arbitrary dimensions. We link the task of entanglement detection in general states to the well-known graph-theoretic problem of finding triangle-free-induced subgraphs in a given graph.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon application of a local averaging operation, the separability of such states transforms into a simple matrix positivity condition, the violation of which implies the presence of entanglement. We completely characterize the class of triangle-free graphs which allows for nontrivial entanglement detection using the above test. Moreover, we develop a recipe to construct a plethora of unique classes of positive partial transpose (PPT) entangled triangle-free states in arbitrary dimensions. Finally, we link the task of entanglement detection in general states to the well-known graph-theoretic problem of finding triangle-free-induced subgraphs in a given graph.

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