Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses

Abstract

We theoretically study the quantum Fisher information (QFI) of the SU(1,1) interferometer with phase shifts in two arms taking account of realistic noise effects. A generalized phase transform including the phase diffusion effect is presented by the purification process. Based on this transform, the analytical QFI and the bound to the quantum precision are derived when considering the effects of phase diffusion and photon losses simultaneously. To beat the standard quantum limit with the reduced precision of phase estimation due to noisy, the upper bounds of decoherence coefficients as a function of total mean photon number are given.

Ancilla-assisted schemes are beneficial for Gaussian state phase estimation

“…The SU (1,1) interferometer has been extensively studied (see, for example, Refs. [14,[22][23][24] and here we show that in the high noise regime, at least for some parameter space, the ancilla-assisted scheme outperforms both the SU (1,1) and the coherent state. Another ancilla-assisted scheme has been considered in Ref.…”

“…In optical interferometry, a coherent-light-based strategy is most commonly used but its sensitivity for phase estimation is shot-noise limited, namely ϕ 2 N −1 . If one needs to achieve a finer precision given a finite amount of resources, one has to resort to interferometry with nonclassical states, such as the coherent squeezed state [9], two-mode squeezedvacuum [10,11], NOON states [12], and squeezed vacuum states [13][14][15]. For works relating to Gaussian state quantum metrology, see, e.g., Refs.…”

Spectrally multimode integrated SU(1,1) interferometer

“…Hence, it is more convenient to calculate the relevant quantities by using the output annihilation and creation operators expressed in the plane wave basis, introduced in [29] and directly presented in Appendix, see Eq. (28). Using the output plane wave operators Eq.…”

“…These studies have shown that it is generally possible to overcome the shot noise limit and even reach the Heisenberg limit. Moreover, SU(1,1) interferometers can provide different benefits with respect to other interferometers, not only in terms of high-precision measurements, but also because of the possibility to perform a joint measurement of multiple observables [24] and due to the advantages of robustness against external losses, namely losses due to an inefficient detection system [25,26,27,28].…”

Effects of losses on the sensitivity of an actively correlated Mach-Zehnder interferometer

“…For SU (1,1) interferometer, the beam splitters in the MZI are replaced by nonlinear beam splitter such as an optical parametric amplifier (PA) or a four-wave mixers, which are mathematically characterized by the group SU (1,1). Because the sensitivities of these interferometers can achieve Heisenberg limit, this type of interferometers have received extensive attention both experimentally [8][9][10][11][12][13][14][15][16][17] and theoretically [18][19][20][21][22][23][24][25][26][27][28][29].…”