Cloning of a quantum measurement

TL;DR

This paper investigates optimal quantum algorithms for cloning and learning an unknown measurement device, providing theoretical analysis and a practical quantum network implementation for the task.

Contribution

It introduces a comprehensive analysis of quantum measurement cloning and learning, including optimal strategies and a simple network for 1 -> 2 cloning.

Findings

Optimal strategies for measurement cloning and learning are derived.

A simple quantum network for 1 -> 2 measurement cloning is proposed.

The analysis applies to arbitrary Hilbert space dimensions.

Abstract

We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1 -> 2 learning of the measurement, otherwise the task is called 1 -> 2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension of the Hilbert space. For 1 -> 2 cloning we also propose a simple quantum network that realizes the optimal strategy.