Optimal phase estimation in quantum networks

TL;DR

This paper investigates optimal strategies for estimating a phase in quantum networks, optimizing both input states and measurements, with the optimal measurement related to quantum Fourier transforms, applicable in various quantum information tasks.

Contribution

It introduces a method to optimize phase estimation in quantum networks by jointly optimizing input states and measurements, revealing the optimal POVM as a quantum Fourier transform.

Findings

Optimal POVM is equivalent to a quantum Fourier transform.

Joint optimization of input states and measurements improves phase estimation.

Applications demonstrated in quantum information processing.

Abstract

We address the problem of estimating the phase phi given N copies of the phase rotation u(phi) within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the N phase rotations, and ending with a POVM. We optimise the POVM for a given input state and fixed arrangement. Then we also optimise the input state for some specific cost functions. In all cases, the optimal POVM is equivalent to a quantum Fourier transform in an appropriate basis. Examples and applications are given.