Analysis of the super-sensitivity of N00N and M−and−M′ states under atmospheric influence

Abstract

Quantum Sensors like Quantum Radar and Lidar based on the interference of non-classical states can achieve super-sensitivity beyond the Standard Quantum Limit (SQL). But as the photons transporting in atmosphere, the environmental interaction causes quantum de-coherence and results in the reduction of super-sensitivity range of the quantum sensors. The most significant effect of atmospheric transmission is photon loss along with phase fluctuation. In this letter, we introduce both the photon loss and phase fluctuation by adding a fictitious beam splitter in the signal arm of Mach- Zehnder interferometer (MZI). The density matrix with N00N and M&M' entangled states being the input states under the condition of photon loss and phase fluctuation is given respectively. Then as the optimal detection schemes parity operator is used as the detector and the formula of the sensitivity is derived. The super-sensitivity range of M&M’ and N00N states with de-coherence are simulated. As a consequence, with high photon loss M&M’ states shows the better phase sensitivity than N00N states but the N00N state is better when the loss is smaller than 20%. And with pure phase fluctuations N00N states get the longer range. M&M’ states is sensitive to the transmittance difference between two arms of the interferometer.