Fast universal performance certification of measurement schemes for quantum tomography

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33159811" target="_blank" >RIV/61989592:15310/16:33159811 - isvavai.cz</a>
Result on the web
<a href="http://journals.aps.org/pra/pdf/10.1103/PhysRevA.94.022113" target="_blank" >http://journals.aps.org/pra/pdf/10.1103/PhysRevA.94.022113</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevA.94.022113" target="_blank" >10.1103/PhysRevA.94.022113</a>

Result language
angličtina
Original language name
Fast universal performance certification of measurement schemes for quantum tomography
Original language description
Prior to a measurement in a quantum-state tomography experiment, it is important to evaluate the performance of this measurement with respect to the average accuracy in state estimation. We propose a fast and reliable numerical certification of measurement performance that is applicable to any known quantum measurement. This numerical method is based on the statistical theory of unbiased estimation that is valid for any physically accessible quantum state that is necessarily full rank in the limit of a large number of measurement copies, and the Hoeffding inequality that applies to bounded statistical quantities in the quantum state space. We present the use of this straightforward certification procedure by illustrating the convergence to optimal pure-state tomography with an increasing number of overcomplete measurement outcomes. Furthermore, we demonstrate that the performances of symmetric informationally complete measurements and mutually unbiased bases, which are commonly regarded as optimal measurements, can be easily beaten in tomographic performance with randomly generated measurements that are only slightly more informationally overcomplete. Two important classes of random measurements are also discussed with the help of our numerical machinery.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BH - Optics, masers and lasers
OECD FORD branch
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Project
<a href="/en/project/GA15-03194S" target="_blank" >GA15-03194S: Informationally complete observations for information processing with random light</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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