Nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound for coherent states

Abstract

Quantum-enhanced phase estimation paves the way to ultra-precision sensing and is of great realistic significance. In this paper we investigate theoretically the estimation of a second-order nonlinear phase shift using a coherent state and parity measurement. A numerical expression is derived, the resolution and sensitivity of parity signal are contrasted to linear phase estimation protocol, and the signal visibility is analyzed. Additionally, by virtue of phase-averaging approach to eliminate any hidden resources, we make an attempt at unveiling the low-down on the fundamental sensitivity limit from quantum Fisher information. Finally, the effects of several realistic scenarios on the resolution and the sensitivity are studied, including photon loss, imperfect detector, and those which are a combination thereof.

Supersensitivity of Kerr phase estimation with two-mode squeezed vacuum states

“…We also identify that parity detection is a nearly optimal measurement for saturating the phase sensitivities we derived. Our results suggest that the scheme with TMSV states is highly superior to the one with coherent states [26] and the sensitivity is enhanced significantly beyond the BGSL [22]. More importantly, this sensitivity superiority effect can still be observed when the photon number becomes large, which is in a sharp contrast with the previous result reported in Ref.…”

“…( 21) and ( 22), as compared to the sensitivities for coherent states as reported in Ref. [26]. The results suggest that both TF and TMSV states outperform coherent states, which is identical with the observation with parity detection shown in previous section.…”

“…3 the result obtained in Ref. [26], in which one input port of the interferometer is injected with a coherent state and another input port is injected with a vacuum state, and a same measurement is considered as done in this manuscript. Our results indicate that TF states outperform coherent states except at a small number of points under the same energy constraint on the input.…”

“…Recently, several works identified that a Heisenberg-limitscaling sensitivity is attainable even without the use of entangled resources in the nonlinear cases [23][24][25]. In another recent work, Zhang et al found that using coherent state of light can beat the Heisenberg limit in Kerr phase estimation [26]. Moreover, Joo et al demonstrated that, entangled coherent states of small photon numbers can outperform NOON states in nonlinear settings, suggesting that the BGSL would be further overcome [27].…”

Phase-sensitive nonclassical properties in quantum metrology with a displaced squeezed vacuum state

“…In Sec. 3, to rule out the overestimation of parameter information [34][35][36][37], we first calculate the QFI of the single-mode DSV state after introducing an external parameter reference. Secondly, based on the results of the DSV's QFI, we investigate how the accuracy limit of parameter estimation changes with respect to the phase-sensitive parameter under some typical displacement and squeezing parameters.…”