Suess, Daniel, Rudnicki, Lukasz, Maciel, Thiago O. and Gross, David (2017). Error regions in quantum state tomography: computational complexity caused by geometry of quantum states. New J. Phys., 19. BRISTOL: IOP PUBLISHING LTD. ISSN 1367-2630
Full text not available from this repository.Abstract
The outcomes of quantum mechanical measurements are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the particularly relevant task of quantum state tomography, it has been shown that a significant reduction in uncertainty can be achieved by taking the positivity of quantum states into account. However-the large number of partial results and heuristics notwithstanding-no efficient general algorithm is known that produces an optimal uncertainty region from experimental data, while making use of the prior constraint of positivity. Here, we provide a precise formulation of this problem and show that the general case is NP-hard. Our result leaves room for the existence of efficient approximate solutions, and therefore does not in itself imply that the practical task of quantum uncertainty quantification is intractable. However, it does show that there exists a non-trivial trade-off between optimality and computational efficiency for error regions. Weprove two versions of the result: one for frequentist and one for Bayesian statistics.
| Item Type: | Journal Article | ||||||||||||||||||||
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| URN: | urn:nbn:de:hbz:38-217514 | ||||||||||||||||||||
| DOI: | 10.1088/1367-2630/aa7ce9 | ||||||||||||||||||||
| Journal or Publication Title: | New J. Phys. | ||||||||||||||||||||
| Volume: | 19 | ||||||||||||||||||||
| Date: | 2017 | ||||||||||||||||||||
| Publisher: | IOP PUBLISHING LTD | ||||||||||||||||||||
| Place of Publication: | BRISTOL | ||||||||||||||||||||
| ISSN: | 1367-2630 | ||||||||||||||||||||
| Language: | English | ||||||||||||||||||||
| Faculty: | Faculty of Mathematics and Natural Sciences | ||||||||||||||||||||
| Divisions: | Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics | ||||||||||||||||||||
| Subjects: | no entry | ||||||||||||||||||||
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| Refereed: | Yes | ||||||||||||||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/21751 |
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