Quantum metrology in the heisenberg limit

Abstract

This study is aimed at quantum measurements with Heisenberg limited sensitivities. The high-precision measurements of length and angle variables have led to the development of many novel techniques, both on theoretical and experimental fronts. Squeezed states which have smaller uncertainties in some variables have long been employed for this use. In many cases, parametric variations translate into the phase variations, which are measured by interferometric means. It has been demonstrated by Zurek that interference effects in the phase space can profitably be used for the measurements of variables, which were otherwise limited by Heisenberg uncertainty principle. For this purpose certain superposed states,viz. Cat and kitten states have been employed. This way of achieving better sensitivity in parameter estimation have experimentally been verified as well, using Cat-like laser beams and has been termed as sub-Fourier sensitivity.In this work, these branches of quantum metrology have been greatly emphasized. The role of entangled states in quantum metrology has also been explored starting from characterization of entanglement to improving sensitivities in more dimensions through an entangled state comprising superposed cat-like states. Lastly, the concept of maximum achievable resolution, is explored through a statistical Cramer-Rao bound. This bound has been calculated for several states and it has been found that pair coherent states have a robust nature with regards to interferometry than many of the commonly used states in an interferometer.