Adversarial vs cooperative quantum estimation

TL;DR

This paper investigates quantum estimation of isometries with two outputs, comparing adversarial and cooperative control, and extends estimation theory to local measurements with applications to two-qubit unitaries.

Contribution

It introduces the concept of privacy in quantum estimation, generalizes Personik's theorem for local measurements, and analyzes estimation strategies for two-qubit unitaries.

Findings

Optimal estimation strategies identified for different control scenarios.

Generalization of Personik's theorem to local measurement cases.

Application of methods to two-qubit unitaries with fixed input states.

Abstract

We address the estimation of a one-parameter family of isometries taking one input into two output systems. This primarily allows us to consider imperfect estimation by accessing only one output system, i.e. through a quantum channel. Then, on the one hand, we consider separate and adversarial control of the two output systems to introduce the concept of \emph{privacy of estimation}. On the other hand we conceive the possibility of separate but cooperative control of the two output systems. Optimal estimation strategies are found according to the minimum mean square error. This also implies the generalization of Personik's theorem to the case of local measurements. Finally, applications to two-qubit unitaries (with one qubit in a fixed input state) are discussed.