3-qubit entanglement: A Jordan algebraic perspective

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It is by now well known that three qubits can be totally entangled in two physically distinct ways. Here we review work classifying the physically distinct forms of 3-qubit entanglement using the elegant framework of Jordan algebras, Freudenthal-Kantor triple systems and groups of type E7. In particular, it is shown that the four Freudenthal-Kantor ranks correspond precisely to the four 3-qubit entanglement classes: (1) Totally separable A-B-C, (2) Biseparable A-BC, B-CA, C-AB, (3) Totally entangled W, (4) Totally entangled GHZ. The rank 4 GHZ class is regarded as maximally entangled in the sense that it has non-vanishing quartic norm, the defining invariant of the Freudenthal-Kantor triple system. While this framework is specific to three qubits, we show here how the essential features may be naturally generalised to an arbitrary number of qubits.

Original languageEnglish
Article number012003
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 2014
Event6th ECM Satellite QQQ Conference 3Quantum: Algebra Geometry Information, QQQ Conference 2012 - Tallinn, Estonia
Duration: 10 Jul 201213 Jul 2012


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