3Quantum: Algebra Geometry Information | |
3-qubit entanglement: A Jordan algebraic perspective | |
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 |
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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.
【 预 览 】
Files | Size | Format | View |
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3-qubit entanglement: A Jordan algebraic perspective | 909KB | download |