Luis Aina, Alfredo2023-06-172023-06-172017-03-132469-992610.1103/PhysRevA.95.032113https://hdl.handle.net/20.500.14352/17777©2017 American Physical Society I thank Dr. Angel Rivas and Dr. Jesus Rubio for enlightening discussions and acknowledge support from Spanish MINECO Grant no. FIS2012-35583 and CAM research consortium QUITEMAD+ Grant No. S2013/ICE-2801.We provide a very simple case showing that the weak form of the Heisenberg limit can be beaten while the prior information is improved without bias.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.95.032113https://journals.aps.orgopen access535Quantum phase measurementsLikelihoodMetrologyÓptica (Física)2209.19 Óptica Física