title: Quantum measurement bounds beyond the uncertainty relations.
abstract: In quantum mechanics, the Heisenberg uncertainty relations and the Cramér-Rao inequalities typically limit the precision in the estimation of a parameter through the standard deviation of a conjugate observable. Here we extend these relations by giving a bound to the precision of a parameter in terms of the expectation value of the conjugate observable. This has both foundational and practical consequences: in quantum optics it resolves a controversy over which is the ultimate precision in interferometry.
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, piazza dei Cavalieri 7, I-56126 Pisa, Italy.
authors.forename: Vittorio
authors.initials: V
authors.lastname: Giovannetti
authors.forename: Seth
authors.initials: S
authors.lastname: Lloyd
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Maccone