dorsal/arxiv
View SchemaTypical entanglement in multi-qubit systems
| Authors | Vivien M Kendon, Kae Nemoto, William J Munro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106023 |
| URL | https://arxiv.org/abs/quant-ph/0106023 |
| DOI | 10.1080/09500340110120914 |
| Journal | J. Mod. Optics, 49 (10), 1709-1716, 2002 |
Abstract
Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood, however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter's concurrence formula) as N increases. Above six qubits very few states have any pairwise entanglement, and generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become PPT (positive partial transpose i.e., separable or only bound entangled) around N >~ 2m + 3, based on numerical analysis up to N=13.
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"abstract": "Quantum entanglement and its paradoxical properties hold the key to an\ninformation processing revolution. Much attention has focused recently on the\nchallenging problem of characterizing entanglement. Entanglement for a two\nqubit system is reasonably well understood, however, the nature and properties\nof multiple qubit systems are largely unexplored. Motivated by the importance\nof such systems in quantum computing, we show that typical pure states of N\nqubits are highly entangled but have decreasing amounts of pairwise\nentanglement (measured using the Wootter\u0027s concurrence formula) as N increases.\nAbove six qubits very few states have any pairwise entanglement, and generally,\nfor a typical pure state of N qubits there is a sharp cut-off where its\nsubsystems of size m become PPT (positive partial transpose i.e., separable or\nonly bound entangled) around N \u003e~ 2m + 3, based on numerical analysis up to\nN=13.",
"arxiv_id": "quant-ph/0106023",
"authors": [
"Vivien M Kendon",
"Kae Nemoto",
"William J Munro"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500340110120914",
"journal_ref": "J. Mod. Optics, 49 (10), 1709-1716, 2002",
"title": "Typical entanglement in multi-qubit systems",
"url": "https://arxiv.org/abs/quant-ph/0106023"
},
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