Quantifying quantum coherence of optical cat states in a noisy channel

Quantum coherence is one of the most fundamental features of quantum mechanics that underlines the unique characteristics of quantum technology. Optical cat state is a superposition of two coherent states and has broad applications in quantum information and quantum metrology. In the application of optical cat state, it is essential to investigate the quantum coherence of it when it interacts with the environment. In this manuscript, we present the quantum coherence of an optical cat state in a noisy channel by calculating the relative entropy in Fock basis. We show that the quantum coherence of an optical cat state is robust against loss and noise in a noisy channel. Different from quantum coherence, the negativity of the Wigner function and the fidelity of the cat state are not robust against loss and noise. Our result provides a reference for applying optical cat states in a noisy environment.