The elusive Heisenberg limit in quantum enhanced metrology

TL;DR

This paper introduces new tools for bounding quantum measurement precision, revealing that decoherence limits quantum enhancement to a constant factor, not quadratic, in practical scenarios.

Contribution

The authors develop efficient, intuitive methods using quantum channel geometry and semi-definite programming to derive bounds on quantum metrology precision under decoherence.

Findings

Quantum enhancement is limited to a constant factor with decoherence.

Derived bounds for dephasing, depolarization, spontaneous emission, and photon loss.

Quantum advantage diminishes significantly in realistic noisy environments.

Abstract

We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account, the maximal possible quantum enhancement amounts generically to a constant factor rather than quadratic improvement. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: dephasing,depolarization, spontaneous emission and photon loss.