Channel Simulation in Quantum Metrology

TL;DR

This review explores how channel simulation techniques, especially quantum teleportation, simplify quantum parameter estimation protocols and establish bounds, highlighting the role of channel types and the challenge of reaching the Heisenberg limit.

Contribution

It introduces a unified framework for channel simulation in quantum metrology, including new results for bosonic Gaussian channels and discusses open problems for achieving the Heisenberg limit.

Findings

Channel simulation simplifies adaptive quantum estimation protocols.

Quantum teleportation enables reduction of complex protocols for certain channels.

Matching bounds for parameter estimation are derived using Choi matrices.

Abstract

In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels, we may express the quantum Cram\'er Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.