Maximum likelihood analysis of multiple quantum phase measurements

Quantum limits on precision measurement of phase

  • Braunstein, S. L., Lane, A. S. and Caves, C. M. (1992): Physical Review Letters 69, 2153-2156.

    ABSTRACT: Shapiro, Shepard, and Wong [Phys. Rev. Lett. 62, 2377 (1989)] suggested that a scheme of multiple phase measurements, using quantum states with minimum "reciprocal peak likelihood," could achieve a phase sensitivity scaling as 1/N_tot^2, where N_tot is the mean number of photons available for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3 < N_tot < 120. A power-law fit to the simulated data yields a phase sensitivity that scales as 1/N_tot^0.85(+/-0.01). We conclude that reciprocal peak likelihood is not a good measure of sensitivity.