### Abstract

In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann curvature and the Fisher information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér–Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.

Original language | English |
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Pages (from-to) | 094010-1-094010-18 |

Number of pages | 18 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2019 |

Publication status | Published - 2019 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Carollo, A., Valenti, D., Spagnolo, B., Carollo, A., Spagnolo, B., Dubkov, A. A., & Valenti, D. (2019). On quantumness in multi-parameter quantum estimation.

*Journal of Statistical Mechanics: Theory and Experiment*,*2019*, 094010-1-094010-18.