Quantum Weiss-Weinstein bounds for quantum metrology

TL;DR

This paper introduces quantum Weiss-Weinstein bounds as a new class of quantum error bounds that can be tighter than traditional quantum Cramér-Rao bounds, especially in non-asymptotic regimes, improving quantum metrology limits.

Contribution

The authors propose quantum Weiss-Weinstein bounds, extending and tightening existing quantum error bounds for more accurate quantum metrology assessments.

Findings

Quantum Weiss-Weinstein bounds include Cramér-Rao bounds as special cases.

The bounds provide a tighter Heisenberg limit for phase estimation.

Demonstrated superiority in non-asymptotic quantum metrology scenarios.

Abstract

Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum Cram\'er-Rao lower error bounds pioneered by Helstrom. Recent work, however, has called into question the tightness of those bounds for highly nonclassical states in the non-asymptotic regime, and better methods are now needed to assess the attainable quantum limits in reality. Here we propose a new class of quantum bounds called quantum Weiss-Weinstein bounds, which include Cram\'er-Rao-type inequalities as special cases but can also be significantly tighter to the attainable error. We demonstrate the superiority of our bounds through the derivation of a Heisenberg limit and phase-estimation examples.