Estimation of a displacement parameter of a quantum system

Peter A. Ivanov

I propose a quantum sensor based on a driven-dissipative quantum system for the joint estimation of two conjugated variables characterizing the phase-space displacement. The quantum probe consists of a lattice system with two-level atoms and bosonic modes which interact via dipolar coupling. Interplay between the coherent dynamics and dissipative processes of losses of bosonic excitations leads to a steady state which exhibits a nonanalytical behavior. I show that close to the dissipative phase transition, the sensitivity of one of the conjugated parameters, i.e., either the magnitude or the phase of the displacement, can be significantly enhanced. Moreover, I show that the sum of the measurement uncertainties of the two parameters can overcome the standard quantum limit.

Alexander Semenovich Holevo

Zhiwei Tao, Yi-Chong Ren, Azezigul Abdukirim +2 more

We predict that the phase-dependent error distribution of locally unentangled quantum states directly affects quantum parameter estimation accuracy. Therefore, we employ the displaced squeezed vacuum (DSV) state as a probe state and investigate an interesting question of the phase-sensitive nonclassical properties in the DSV’s metrology. We found that the accuracy limit of parameter estimation is a function of the phase-sensitive parameter ϕ − θ / 2 with a period π . We show that when ϕ − θ / 2 ∈ [ k π / 2 , 3 k π / 4 ) ( k ∈ Z ) , we can obtain the accuracy of parameter estimation approaching the ultimate quantum limit through the use of the DSV state with the larger displacement and squeezing strength, whereas when ϕ − θ / 2 ∈ ( 3 k π / 4 , k π ] ( k ∈ Z ) , the optimal estimation accuracy can be acquired only when the DSV state degenerates to a squeezed vacuum state.

M. Luanshi, M. B. Malyutov

László Ruppert

Chaohui Zhou, Jun Xin, Yanan Li +1 more

The image of an optical point source is blurred due to light diffraction so that estimating small displacements of the point source with direct imaging demands elaborate processing on the observation data of a camera. Using quantum parameter estimation, we show that for the imaging systems with a real point spread function, any measurement basis constituted by a complete set of real-valued spatial-mode functions is optimal for estimating the displacement. For small displacements, we can concentrate the information about the value of displacement to the measurement of a few spatial modes, which can be selected in terms of the Fisher information distribution. We use digital holography with a phase-only spatial light modulator to implement two simple estimation strategies that are mainly based on the projection measurement of two spatial modes and the readout of a single pixel of a camera.