Besides quantum entanglement and steering, quantum coherence has also been identified as a useful quantum resource in quantum information. It is important to investigate the evolution of quantum coherence in practical quantum channels. In this paper, we experimentally quantify the quantum coherence of a squeezed state and a Gaussian Einstein–Podolsky–Rosen (EPR) entangled state transmitted in Gaussian thermal noise channel. By reconstructing the covariance matrix of the transmitted states, quantum coherence of these Gaussian states is quantified by calculating the relative entropy. We show that quantum coherence of the squeezed state and the Gaussian EPR entangled state is robust against loss and noise in a quantum channel, which is different from the properties of squeezing and Gaussian entanglement. Our experimental results pave the way for application of Gaussian quantum coherence in lossy and noisy environments.

The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the l1 norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.

The uncertainty relation is one of the fundamental principles in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for Gaussian states. Two incompatible continuous-variable observables, amplitude and phase quadratures of an optical mode, are measured simultaneously using a heterodyne measurement system. The EDR values with continuous variables for coherent, squeezed, and thermal states are verified experimentally. Our experimental results demonstrate that Heisenberg’s EDR with continuous variables is violated, while Ozawa’s and Branciard’s EDRs with continuous variables are validated.