Quantum measurement optimization by decomposition of measurements into extremals

Esteban Martínez-Vargas,Carlos Pineda,Pablo Barberis-Blostein

doi:10.1038/s41598-020-65934-w

Esteban Martínez-Vargas, Carlos Pineda + Show 1 more

Open Access

https://doi.org/10.1038/s41598-020-65934-w

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Abstract

Using the convex structure of positive operator value measurements and several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter. This method explores extremal measurements thus providing a significant advantage over previously used methods. We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.

Highlights

Using the convex structure of positive operator value measurements and several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter
If the physical system from which the parameter is to be estimated is analyzed within the framework of quantum mechanics, we shall speak about quantum metrology[1,2,3,4,5]
In this article we specialize to the case of quantum mechanics, where the probability distribution is given by the Born rule and the statistical model is obtained once it is decided which operator is going to be measured

Summary

Introduction

Using the convex structure of positive operator value measurements and several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter. This method explores extremal measurements providing a significant advantage over previously used methods. When a Cramér-Rao type inequality exists, the problem can be reduced to find the extreme of another cost function (for example the Fisher information) over all the quantum measurements This simplifies the problem because it is not longer necessary to maximize over the space of estimators. This method, that we call the random sampling method (RSM), is very inefficient since the POVM space is large

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Conclusion