  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.
