Abstract
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some simple systems in order to track the effect of a local depolarizing noise on the incompatibility of the estimation task. A semidefinite program is described and used to numerically compute the figure of merit when the analytical tools are not sufficient, among these we include an upper bound computable from the symmetric logarithmic derivatives only. Finally we discuss how to obtain compatible models for a general unitary encoding on a finite-dimensional probe.
Highlights
Quantum metrology [1,2,3,4,5] is a special branch of quantum information theory that focuses on the possibility of using quantum effects for improving the accuracy of conventional estimation procedures
Thanks to the huge variety of potential applications, this research field is likely to play a fundamental role in the looming quantum technology revolution
The main goal of quantum metrology is to efficiently plan different types of experiments by minimizing the invested effort to overcome noisy fluctuations that originate by fabrication errors, external fields, microscopic degrees of freedom that are only statistically taken into account, and intrinsic limitations related to the formal structure of the quantum theory itself
Summary
Quantum metrology [1,2,3,4,5] is a special branch of quantum information theory that focuses on the possibility of using quantum effects for improving the accuracy of conventional estimation procedures. The geometric interpretation of the figure of merit is presented in section 3.3 and in section 3.4 we express it in terms of the Holevo-Cramer-Rao bound [19, 41], proved to be achievable thanks to the quantum central limit theorem and the quantum local asymptotic normality (QLAN) [42,43,44,45,46,47,48] This allows us to compute the incompatibility via the semidefinite program (SDP) reported in Appendix C, which is derived from the one presented in [49]. The mathematical environments Definition, Theorem, and Corollary will be used to highlight the most important concepts that we introduce
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