dorsal/arxiv
View SchemaOn the Monomiality of Nice Error Bases
| Authors | Andreas Klappenecker, Martin Roetteler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301078 |
| URL | https://arxiv.org/abs/quant-ph/0301078 |
| Journal | IEEE Transactions on Information Theory, vol. 51, no. 3, pp. 1084 - 1089, 2005 |
Abstract
Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill, which yields nice error bases, and a combinatorial construction by Werner, which yields shift-and-multiply bases. An open problem posed by Schlingemann and Werner (see http://www.imaph.tu-bs.de/qi/problems/6.html) relates these two constructions and asks whether each nice error basis is equivalent to a shift-and-multiply basis. We solve this problem and show that the answer is negative. However, we also show that it is always possible to find a fairly sparse representation of a nice error basis.
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"abstract": "Unitary error bases generalize the Pauli matrices to higher dimensional\nsystems. Two basic constructions of unitary error bases are known: An algebraic\nconstruction by Knill, which yields nice error bases, and a combinatorial\nconstruction by Werner, which yields shift-and-multiply bases. An open problem\nposed by Schlingemann and Werner (see\nhttp://www.imaph.tu-bs.de/qi/problems/6.html) relates these two constructions\nand asks whether each nice error basis is equivalent to a shift-and-multiply\nbasis. We solve this problem and show that the answer is negative. However, we\nalso show that it is always possible to find a fairly sparse representation of\na nice error basis.",
"arxiv_id": "quant-ph/0301078",
"authors": [
"Andreas Klappenecker",
"Martin Roetteler"
],
"categories": [
"quant-ph",
"cs.ET"
],
"journal_ref": "IEEE Transactions on Information Theory, vol. 51, no. 3, pp. 1084\n - 1089, 2005",
"title": "On the Monomiality of Nice Error Bases",
"url": "https://arxiv.org/abs/quant-ph/0301078"
},
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