dorsal/arxiv
View SchemaTypical entanglement of stabilizer states
| Authors | Graeme Smith, Debbie Leung |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510232 |
| URL | https://arxiv.org/abs/quant-ph/0510232 |
| DOI | 10.1103/PhysRevA.74.062314 |
| Journal | Phys. Rev. A 74, 062314 (2006) |
Abstract
How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large the state will be close to maximally entangled with probability exponentially close to one. We provide a similar tight characterization of the entanglement present in the maximally mixed state of a randomly chosen stabilizer code. Finally, we show that typically very few GHZ states can be extracted from a random multipartite stabilizer state via local unitary operations. Our main tool is a new concentration inequality which bounds deviations from the mean of random variables which are naturally defined on the Clifford group.
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"abstract": "How entangled is a randomly chosen bipartite stabilizer state? We show that\nif the number of qubits each party holds is large the state will be close to\nmaximally entangled with probability exponentially close to one. We provide a\nsimilar tight characterization of the entanglement present in the maximally\nmixed state of a randomly chosen stabilizer code. Finally, we show that\ntypically very few GHZ states can be extracted from a random multipartite\nstabilizer state via local unitary operations. Our main tool is a new\nconcentration inequality which bounds deviations from the mean of random\nvariables which are naturally defined on the Clifford group.",
"arxiv_id": "quant-ph/0510232",
"authors": [
"Graeme Smith",
"Debbie Leung"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.062314",
"journal_ref": "Phys. Rev. A 74, 062314 (2006)",
"title": "Typical entanglement of stabilizer states",
"url": "https://arxiv.org/abs/quant-ph/0510232"
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