Deterministic quantum phase estimation beyond the ideal NOON state limit

The measurement of physical parameters is one of the main pillars of science. A classic example is the measurement of the optical phase enabled by optical interferometry where the best sensitivity achievable with N photons scales as 1/N - known as the Heisenberg limit . To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex NOON states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with NOON states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a phase estimation scheme based on a deterministic source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the performance of an ideal, and thus unrealistic, NOON state protocol. Using a high-efficiency setup with a total loss of about 11% we achieve a Fisher Information of 15.8(6) rad^2 per photon unparalleled by any other optical phase estimation technology. The work represents a fundamental achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.