### Abstract

Theroblem of estimating aarameter of a quantum system through a series of measurementserformed sequentially on a quantumrobe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. Weresent a generalization of the central limit theorem in theresent context, which under fairly general assumptions shows that as the number N of measurement data increases therobability distribution of functionals of the data (e.g., the average of the data) through which the targetarameter is estimated becomes asymptotically normal and independent of the initial state of therobe. At variance with therevious studies (Guţə M 2011 Phys. Rev. A 83 062324; van Horssen M and Guţə M 2015 J. Math. Phys. 56 022109) we take a diagrammatic approach, which allows one to compute not only the leading orders in N of the moments of the average of the data but also those of the correlations among subsequent measurement outcomes. Inarticular our analysisoints out that the latter, which are not available in usual i.i.d. data, can be exploited in order to improve the accuracy of thearameter estimation. An explicit application of our scheme is discussed by studying how the temperature of a thermal reservoir can be estimated via sequential measurements on a quantumrobe in contact with the reservoir.

Original language | English |
---|---|

Article number | 113055 |

Journal | New Journal of Physics |

Volume | 17 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2015 Nov 27 |

### Fingerprint

### Keywords

- asymptotic normality
- central limit theorem
- Fisher information
- quantum ergodicity
- quantum estimation
- quantum information
- quantum metrology

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*17*(11), [113055]. https://doi.org/10.1088/1367-2630/17/11/113055

**Quantum estimation via sequential measurements.** / Burgarth, Daniel; Giovannetti, Vittorio; Kato, Airi N.; Yuasa, Kazuya.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 17, no. 11, 113055. https://doi.org/10.1088/1367-2630/17/11/113055

}

TY - JOUR

T1 - Quantum estimation via sequential measurements

AU - Burgarth, Daniel

AU - Giovannetti, Vittorio

AU - Kato, Airi N.

AU - Yuasa, Kazuya

PY - 2015/11/27

Y1 - 2015/11/27

N2 - Theroblem of estimating aarameter of a quantum system through a series of measurementserformed sequentially on a quantumrobe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. Weresent a generalization of the central limit theorem in theresent context, which under fairly general assumptions shows that as the number N of measurement data increases therobability distribution of functionals of the data (e.g., the average of the data) through which the targetarameter is estimated becomes asymptotically normal and independent of the initial state of therobe. At variance with therevious studies (Guţə M 2011 Phys. Rev. A 83 062324; van Horssen M and Guţə M 2015 J. Math. Phys. 56 022109) we take a diagrammatic approach, which allows one to compute not only the leading orders in N of the moments of the average of the data but also those of the correlations among subsequent measurement outcomes. Inarticular our analysisoints out that the latter, which are not available in usual i.i.d. data, can be exploited in order to improve the accuracy of thearameter estimation. An explicit application of our scheme is discussed by studying how the temperature of a thermal reservoir can be estimated via sequential measurements on a quantumrobe in contact with the reservoir.

AB - Theroblem of estimating aarameter of a quantum system through a series of measurementserformed sequentially on a quantumrobe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. Weresent a generalization of the central limit theorem in theresent context, which under fairly general assumptions shows that as the number N of measurement data increases therobability distribution of functionals of the data (e.g., the average of the data) through which the targetarameter is estimated becomes asymptotically normal and independent of the initial state of therobe. At variance with therevious studies (Guţə M 2011 Phys. Rev. A 83 062324; van Horssen M and Guţə M 2015 J. Math. Phys. 56 022109) we take a diagrammatic approach, which allows one to compute not only the leading orders in N of the moments of the average of the data but also those of the correlations among subsequent measurement outcomes. Inarticular our analysisoints out that the latter, which are not available in usual i.i.d. data, can be exploited in order to improve the accuracy of thearameter estimation. An explicit application of our scheme is discussed by studying how the temperature of a thermal reservoir can be estimated via sequential measurements on a quantumrobe in contact with the reservoir.

KW - asymptotic normality

KW - central limit theorem

KW - Fisher information

KW - quantum ergodicity

KW - quantum estimation

KW - quantum information

KW - quantum metrology

UR - http://www.scopus.com/inward/record.url?scp=84951335712&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951335712&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/17/11/113055

DO - 10.1088/1367-2630/17/11/113055

M3 - Article

AN - SCOPUS:84951335712

VL - 17

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 11

M1 - 113055

ER -