dorsal/arxiv
View SchemaReal Mutually Unbiased Bases
| Authors | P. Oscar Boykin, Meera Sitharam, Mohamad Tarifi, Pawel Wocjan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502024 |
| URL | https://arxiv.org/abs/quant-ph/0502024 |
Abstract
We tabulate bounds on the optimal number of mutually unbiased bases in R^d. For most dimensions d, it can be shown with relatively simple methods that either there are no real orthonormal bases that are mutually unbiased or the optimal number is at most either 2 or 3. We discuss the limitations of these methods when applied to all dimensions, shedding some light on the difficulty of obtaining tight bounds for the remaining dimensions that have the form d=16n^2, where n can be any number. We additionally give a simpler, alternative proof that there can be at most d/2+1 real mutually unbiased bases in dimension d instead of invoking the known results on extremal Euclidean line sets by Cameron and Seidel, Delsarte, and Calderbank et al.
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"abstract": "We tabulate bounds on the optimal number of mutually unbiased bases in R^d.\nFor most dimensions d, it can be shown with relatively simple methods that\neither there are no real orthonormal bases that are mutually unbiased or the\noptimal number is at most either 2 or 3. We discuss the limitations of these\nmethods when applied to all dimensions, shedding some light on the difficulty\nof obtaining tight bounds for the remaining dimensions that have the form\nd=16n^2, where n can be any number. We additionally give a simpler, alternative\nproof that there can be at most d/2+1 real mutually unbiased bases in dimension\nd instead of invoking the known results on extremal Euclidean line sets by\nCameron and Seidel, Delsarte, and Calderbank et al.",
"arxiv_id": "quant-ph/0502024",
"authors": [
"P. Oscar Boykin",
"Meera Sitharam",
"Mohamad Tarifi",
"Pawel Wocjan"
],
"categories": [
"quant-ph"
],
"title": "Real Mutually Unbiased Bases",
"url": "https://arxiv.org/abs/quant-ph/0502024"
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