  Path-entangled multi-photon states allow optical phase-sensing beyond the
shot-noise limit, provided that an efficient parity measurement can be
implemented. Realising this experimentally is technologically demanding, as it
requires coincident single-photon detection proportional to the number of
photons involved, which represents a severe challenge for achieving a practical
quantum advantage over classical methods. Here, we exploit advanced quantum
state engineering based on superposing two photon-pair creation events to
realise a new approach that bypasses this issue. In particular, optical phase
shifts are probed with a two-photon quantum state whose information is
subsequently effectively transferred to a single-photon state. Notably, without
any multiphoton detection, we infer phase shifts by measuring the average
intensity of the single-photon beam on a photodiode, in analogy to standard
classical measurements. Importantly, our approach maintains the quantum
advantage: twice as many interference fringes are observed for the same phase
shift, corresponding to N=2 path-entangled photons. Our results demonstrate
that the advantages of quantum-enhanced phase-sensing can be fully exploited in
standard intensity measurements, paving the way towards resource-efficient and
practical quantum optical metrology.
