Quantum learning algorithms for quantum measurements

TL;DR

This paper investigates quantum learning algorithms for quantum measurements, deriving optimal strategies for limited training examples and revealing that learning measurements requires quantum memory, unlike learning unitary gates.

Contribution

It provides the first optimal learning algorithms for von Neumann measurements with one or two examples and shows the necessity of quantum memory for learning measurements.

Findings

Optimal algorithms for one and two training examples.

Learning measurements cannot be parallelized, unlike unitary gates.

Quantum memory is essential for learning quantum measurements.

Abstract

We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information.