Asymmetric entanglement for quantum target sensing

Entanglement is beneficial to enhancing a phase sensitivity beyond the classical limit that is given by a coherent state. The best performance is achieved with symmetric entangled states, which is enhanced further by sending more photons to the signal mode. We delve into which entanglement structure is valuable for quantum target sensing, such as a reflectivity parameter. We show that an asymmetric entangled state can approach the local joint measurement bound of a two-mode squeezed vacuum state which is a nearly optimal input state for quantum target sensing, whereas it cannot beat the performance of the coherent state for quantum phase sensing. The result is demonstrated with an asymmetric entangled coherent state whose performance is evaluated with quantum Fisher information and confirmed by the signal-to-noise ratio with an optimal observable. The best quantum advantage is achieved in the case of sending fewer photons to the signal mode and many more photons to the idler mode.

Figure 1

Schematic of quantum target sensing (upper panel), where the thermal-noise environment is displayed with a thick orange line. Generation of an asymmetric entangled coherent state with an even-cat state and a beam splitter having $t^2+r^2=1, \alpha =t{\alpha }_1$ and $\beta =r{\alpha }_1$ (lower panel).

Figure 2

Quantum advantage (QA) region for an asymmetric entangled coherent state. CB presents the classical bound with a coherent state. $N_S$ ($N_I$) is the signal (idler) mean photon number. Quantum Fisher information as a function of signal mean photon number for quantum reflectivity sensing (lower panel), where the blue solid curve represents an asymmetric entangled coherent state (AECS) with $N_I=10$. $N_B$ is the mean photon number of thermal noise.