Quantum measurement bounds beyond uncertainty relations

Quantum measurements are limited by bounds such as the Heisenberg uncertainty relations which limit the accuracy of measuring a quantity via the standard deviation of the conjugate one. This talk shows that the accuracy of measuring a quantity such as phase or time is limited by the expectation value of the conjugate quantity. This result proves the long-standing conjecture -- recently challenged -- that the ultimate phase-precision limit in interferometry is lower bounded by the inverse of the total number of photons employed in the estimation process.