Quantum Weiss-Weinstein bounds for quantum metrology

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, for decades researchers have relied on the quantum Cramér-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 Cramér-Rao-type inequalities as special cases but can also be significantly tighter to the attainable error.Wedemonstrate the superiority of our bounds through the derivation of a Heisenberg limit and phase estimation examples.