1105.2990 (Y. R. Zhang et al.)

Proper form of Heisenberg limit of phase measurement    [PDF]

Y. R. Zhang, G. R. Jin, J. P. Cao, W. M. Liu, H. Fan

We investigate the appropriate form of Heisenberg limit in linear two-path interferometer phase measurement. We propose that the bound of the phase uncertainty should take the form as, $1/<\hat{N}^{2}>^{1/2}$, which applies for cases with both fixed and fluctuating number of particles. We present a specified superposed state with arbitrary high phase sensitivity but with a finite average photon number, and it apparently breaks the known Heisenberg limit of phase sensitivity in form $1/<\hat{N}>$ for case of fixed number of particles, however, saturates the bound $1/<\hat{N}^{2}>^{1/2}$. We indicate that only superposed NOON states by simultaneous measurements can achieve this limit, and our result also shows that quantum Fisher information is saturated by a positive operator value measurement (POVM) in linear two-path interferometer phase measurement.

View original: http://arxiv.org/abs/1105.2990