RT Journal Article T1 Sub-Heisenberg estimation of non-random phase shifts A1 Rivas Vargas, Ángel A1 Luis Aina, Alfredo AB We provide evidence that the uncertainty in detection of small and deterministic phase-shift deviations from a working point can be lower than the Heisenberg bound, for a fixed finite mean number of photons. We achieve that by exploiting nonlinearity of estimators and coherence with the vacuum. PB IOP Publishing SN 1367-2630 YR 2012 FD 2012 LK https://hdl.handle.net/20.500.14352/44589 UL https://hdl.handle.net/20.500.14352/44589 LA eng NO © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We are grateful to Professors A Smerzi, L Maccone, M Tsang and M J W Hall for useful discussions. We acknowledge financial support from the project QUITEMAD S2009-ESP-1594 of the Consejeria de Educacion de la Comunidad de Madrid. AR acknowledges support from MICINN FIS2009-10061. AL acknowledges support from project no. FIS2008-01267 of the Spanish Direccion General de Investigacion del Ministerio de Ciencia e Innovacion. NO Comunidad de Madrid NO Ministerio de Ciencia e Innovacion (MICINN), España DS Docta Complutense RD 17 abr 2025