### 摘要

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.

原文 | English |
---|---|

文章編號 | 032309 |

期刊 | Physical Review A |

卷 | 97 |

發行號 | 3 |

DOIs | |

出版狀態 | Published - 2018 三月 12 |

### 指紋

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### 引用此文

*Physical Review A*,

*97*(3), [032309]. https://doi.org/10.1103/PhysRevA.97.032309

}

*Physical Review A*, 卷 97, 編號 3, 032309. https://doi.org/10.1103/PhysRevA.97.032309

**Device-independent point estimation from finite data and its application to device-independent property estimation.** / Lin, Pei Sheng; Rosset, Denis; Zhang, Yanbao; Bancal, Jean Daniel; Liang, Yeong Cherng.

研究成果: Article

TY - JOUR

T1 - Device-independent point estimation from finite data and its application to device-independent property estimation

AU - Lin, Pei Sheng

AU - Rosset, Denis

AU - Zhang, Yanbao

AU - Bancal, Jean Daniel

AU - Liang, Yeong Cherng

PY - 2018/3/12

Y1 - 2018/3/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85043980498&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043980498&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.97.032309

DO - 10.1103/PhysRevA.97.032309

M3 - Article

AN - SCOPUS:85043980498

VL - 97

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 032309

ER -