dorsal/arxiv
View SchemaEntropic uncertainty relations and locking: tight bounds for mutually unbiased bases
| Authors | Manuel A. Ballester, Stephanie Wehner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606244 |
| URL | https://arxiv.org/abs/quant-ph/0606244 |
| DOI | 10.1103/PhysRevA.75.022319 |
| Journal | Phys. Rev. A 75, 022319 (2007) |
Abstract
We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to sqrt{d} measurements in mutually unbiased bases. We then show that using more mutually unbiased bases does not always lead to a better locking effect. We prove that the optimal bound for the accessible information using up to sqrt{d} specific mutually unbiased bases is log d/2, which is the same as can be achieved by using only two bases. Our result indicates that merely using mutually unbiased bases is not sufficient to achieve a strong locking effect, and we need to look for additional properties.
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"abstract": "We prove tight entropic uncertainty relations for a large number of mutually\nunbiased measurements. In particular, we show that a bound derived from the\nresult by Maassen and Uffink for 2 such measurements can in fact be tight for\nup to sqrt{d} measurements in mutually unbiased bases. We then show that using\nmore mutually unbiased bases does not always lead to a better locking effect.\nWe prove that the optimal bound for the accessible information using up to\nsqrt{d} specific mutually unbiased bases is log d/2, which is the same as can\nbe achieved by using only two bases. Our result indicates that merely using\nmutually unbiased bases is not sufficient to achieve a strong locking effect,\nand we need to look for additional properties.",
"arxiv_id": "quant-ph/0606244",
"authors": [
"Manuel A. Ballester",
"Stephanie Wehner"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.022319",
"journal_ref": "Phys. Rev. A 75, 022319 (2007)",
"title": "Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases",
"url": "https://arxiv.org/abs/quant-ph/0606244"
},
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