Improved linear and Kerr nonlinear phase estimation via photon addition operations

TL;DR

This paper demonstrates that combining photon addition operations with Kerr nonlinear phase shifters in a Mach-Zehnder interferometer significantly improves phase measurement accuracy and robustness against photon loss, approaching the Heisenberg limit.

Contribution

It introduces a novel approach using photon-added non-Gaussian states and Kerr nonlinearities to enhance quantum phase estimation beyond previous methods.

Findings

Photon addition operations improve phase sensitivity and quantum Fisher information.

Combining photon addition with Kerr nonlinearities further enhances measurement accuracy.

The approach increases robustness against photon loss, approaching the Heisenberg limit.

Abstract

The accuracy of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shifters. Here, we employ coherent state mixed photon-added squeezed vacuum state as input into a Mach-Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement accuracy. Our research focuses on phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information. The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and quantum Fisher information, and the measurement accuracy can even approach the Heisenberg limit. In addition, we delve deeper into the scenario of replacing the linear phase shifter with a Kerr nonlinear one and systematically analyze the quantum Fisher information under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shifter can further significantly enhance phase measurement accuracy while effectively improving the system's robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.