dorsal/arxiv
View SchemaSeparable balls around the maximally mixed multipartite quantum states
| Authors | Leonid Gurvits, Howard Barnum |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302102 |
| URL | https://arxiv.org/abs/quant-ph/0302102 |
| DOI | 10.1103/PhysRevA.68.042312 |
| Journal | Phys. Rev. A 68, 042312 (2003) |
Abstract
We show that for an m-partite quantum system, there is a ball of radius 2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices. This can be used to derive an epsilon below which mixtures of epsilon of any density matrix with 1 - epsilon of the maximally mixed state will be separable. The epsilon thus obtained is exponentially better (in the number of systems) than existing results. This gives a number of qubits below which NMR with standard pseudopure-state preparation techniques can access only unentangled states; with parameters realistic for current experiments, this is 23 qubits (compared to 13 qubits via earlier results). A ball of radius 1 is obtained for multipartite states separable over the reals.
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"abstract": "We show that for an m-partite quantum system, there is a ball of radius\n2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable\n(unentangled) positive semidefinite matrices. This can be used to derive an\nepsilon below which mixtures of epsilon of any density matrix with 1 - epsilon\nof the maximally mixed state will be separable. The epsilon thus obtained is\nexponentially better (in the number of systems) than existing results. This\ngives a number of qubits below which NMR with standard pseudopure-state\npreparation techniques can access only unentangled states; with parameters\nrealistic for current experiments, this is 23 qubits (compared to 13 qubits via\nearlier results). A ball of radius 1 is obtained for multipartite states\nseparable over the reals.",
"arxiv_id": "quant-ph/0302102",
"authors": [
"Leonid Gurvits",
"Howard Barnum"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.042312",
"journal_ref": "Phys. Rev. A 68, 042312 (2003)",
"title": "Separable balls around the maximally mixed multipartite quantum states",
"url": "https://arxiv.org/abs/quant-ph/0302102"
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