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Borromean entanglement revisited. (English) Zbl 1214.81046
Kawauchi, Akio (ed.), Knot theory for scientific objects. Proceedings of the international workshop on knot theory for scientific objects, Osaka, Japan, March 8–10, 2006. Osaka: Osaka Municipal Universities Press (ISBN 978-4-901409-29-2/hbk). OCAMI Studies 1, 17-26 (2007).
Summary: An interesting analogy between quantum entangled states and topological links was suggested by P. K. Aravind [Quantum mechanical studies for Abner Shimony. Vol. 2. Dordrecht: Kluwer Academic Publishers. Boston Stud. Philos. Sci. 194, 53–59 (1997; Zbl 1006.81504)]. In particular, he emphasized a connection between the Greenberger-Horne-Zeilinger (GHZ) state and the Borromean rings. However, he made the connection in a way that depends on the choice of measurement basis. We reconsider it in a basis-independent way by using the reduced density matrix.
For the entire collection see [Zbl 1203.00025].

##### MSC:
 81P40 Quantum coherence, entanglement, quantum correlations 57M25 Knots and links in the $$3$$-sphere (MSC2010) 81P15 Quantum measurement theory, state operations, state preparations