dorsal/arxiv
View SchemaThe twistor geometry of three-qubit entanglement
| Authors | Peter Levay |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403060 |
| URL | https://arxiv.org/abs/quant-ph/0403060 |
| DOI | 10.1103/PhysRevA.71.012334 |
Abstract
A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric ${\cal Q}$ a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of ${\cal Q}$. An invariant vanishing for the $GHZ$ class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.
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"abstract": "A geometrical description of three qubit entanglement is given. A part of the\ntransformations corresponding to stochastic local operations and classical\ncommunication on the qubits is regarded as a gauge degree of freedom. Entangled\nstates can be represented by the points of the Klein quadric ${\\cal Q}$ a space\nknown from twistor theory. It is shown that three-qubit invariants are\nvanishing on special subspaces of ${\\cal Q}$. An invariant vanishing for the\n$GHZ$ class is proposed. A geometric interpretation of the canonical\ndecomposition and the inequality for distributed entanglement is also given.",
"arxiv_id": "quant-ph/0403060",
"authors": [
"Peter Levay"
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"doi": "10.1103/PhysRevA.71.012334",
"title": "The twistor geometry of three-qubit entanglement",
"url": "https://arxiv.org/abs/quant-ph/0403060"
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