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Device-independent point estimation from finite data and its application to device-independent property estimation

Lin, Pei-Sheng and Rosset, Denis and Zhang, Yanbao and Bancal, Jean-Daniel and Liang, Yeong-Cherng. (2018) Device-independent point estimation from finite data and its application to device-independent property estimation. Physical Review A , 97. 032309.

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Official URL: https://edoc.unibas.ch/69024/

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Abstract

The device-independent approach to physics is one where conclusions are drawn directly from the observed correlations between measurement outcomes. In quantum information, this approach allows one to make strong statements about the properties of the underlying systems or devices solely via the observation of Bell-inequality-violating correlations. However, since one can only perform a finite number of experimental trials, statistical fluctuations necessarily accompany any estimation of these correlations. Consequently, an important gap remains between the many theoretical tools developed for the asymptotic scenario and the experimentally obtained raw data. In particular, a physical and concurrently practical way to estimate the underlying quantum distribution has so far remained elusive. Here, we show that the natural analogs of the maximum-likelihood estimation technique and the least-square-error estimation technique in the device-independent context result in point estimates of the true distribution that are physical, unique, computationally tractable, and consistent. They thus serve as sound algorithmic tools allowing one to bridge the aforementioned gap. As an application, we demonstrate how such estimates of the underlying quantum distribution can be used to provide, in certain cases, trustworthy estimates of the amount of entanglement present in the measured system. In stark contrast to existing approaches to device-independent parameter estimations, our estimation does not require the prior knowledge of any Bell inequality tailored for the specific property and the specific distribution of interest.
Faculties and Departments:05 Faculty of Science > Departement Physik > Physik > Quantum Physics (Sangouard)
UniBasel Contributors:Bancal, Jean-Daniel
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Physical Society
ISSN:1050-2947
e-ISSN:1094-1622
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:16 Oct 2019 13:14
Deposited On:11 Oct 2019 12:35

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