3-qubit entanglement: A Jordan algebraic perspective

3Quantum: Algebra Geometry Information

物理学;数学

Borsten, L.^1

Blackett Laboratory, Imperial College, London

SW7 2AZ, United Kingdom^1

关键词: 3-qubit entanglement;    Arbitrary number;    Essential features;    Jordan algebra;    Triple system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012003/pdf
DOI  :  10.1088/1742-6596/532/1/012003

来源: IOP

【 摘 要 】

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.