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Ingemar Bengtsson, Markus Grassl, and Gary McConnell.
SIC-POVMs from Stark units: Dimension dimensions n2+3=4p, p prime.
preprint arXiv:2403.02872 [quant-ph]
| dimension d=n2+3 | symmetry | degree | Magma | numerical | |
|---|---|---|---|---|---|
| n | d | ||||
| 3 | 12 | 1 | |||
| 5 | 28 | 1 | 6 | ||
| 7 | 52 | 1 | 12 | ||
| 11 | 124 | 5 | 6 | ||
| 13 | 172 | 1 | 42 | ||
| 17 | 292 | 1 | 72 | ||
| 25 | 628 | 1 | 312 | ||
| 29 | 844 | 7 | 30 | ||
| 31 | 964 | 1 | 480 | ||
| 35 | 1228 | 1 | 918 | ||
| 41 | 1684 | 1 | 840 | ||
| 43 | 1852 | 1 | 924 | ||
| 49 | 2404 | 1 | 2400 | ||
| 55 | 3028 | 1 | 3024 | ||
| 67 | 4492 | 1 | 3366 | ||
| 139 | 19324 | 1 | 4830 | ||
| 199 | 39604 | 11 | 900 | ||
Marcus Appleby, Ingemar Bengtsson, Markus Grassl, Michael Harrison, and Gary McConnell.
SIC-POVMs from Stark units: Prime dimensions n2+3.
Journal of Mathematical Physics, vol. 63, no. 11, November 2022, 112205.
DOI: 10.1063/5.0083520 (open access)
preprint arXiv:2112.05552 [quant-ph]
| dimension d=n2+3 | symmetry | degree | numerical | |
|---|---|---|---|---|
| n | d | |||
| 2 | 7 | 6 | 4 | |
| 4 | 19 | 18 | 4 | |
| 8 | 67 | 6 | 44 | |
| 10 | 103 | 6 | 136 | |
| 14 | 199 | 18 | 44 | |
| 22 | 487 | 6 | 628 | |
| 28 | 787 | 6 | 524 | |
| 38 | 1447 | 6 | 1928 | |
| 50 | 2503 | 6 | 6672 | |
| 52 | 2707 | 6 | 1804 | |
| 64 | 4099 | 6 | 2732 | |
| 76 | 5779 | 54 | 418 | |
| 140 | 19603 | 18 | 4356 | |
Markus Grassl and Andrew J. Scott,
"Fibonacci-Lucas SIC-POVMs",
Journal of Mathematical Physics, vol. 58, no. 12, 122201, December 2017.
DOI: 10.1063/1.4995444
Preprint arXiv:1707.02944 [quant-ph]
| dimension | symmetry | numerical | exact | Magma | degree |
|---|---|---|---|---|---|
| 4 | 6 | 4a (150 digits) | 4a | 4a | 16 |
| 8 | 12 | 8b (150 digits) | 8b | 8b | 32 |
| 19 | 18 | 19e (150 digits) | 19e | 19e | 72 |
| 48 | 24 | 48g (150 digits) | 48g | 48g | 512 |
| 124 | 30 | 124a (150 digits) | 124a | 124a | 2880 |
| 323 | 36 | 323c (150 digits) | 323c | 323c | 10368 |
| 844 | 42 | 844a (150 digits) | 100800 |
Please note that the numerical and the exact SIC-POVMs for dimension 323 differ.
A. J. Scott, M. Grassl.
"Symmetric informationally complete positive-operator-valued measures: A new computer study",
Journal of Mathematical Physics, vol. 51, no. 4, 042203, April 2010.
DOI: 10.1063/1.3374022
Preprint arXiv:0910.5784 [quant-ph]