A hybrid entangled state that involves both discrete and continuous degrees of freedom is a key resource for hybrid quantum information processing. It is essential to characterize entanglement and quantum coherence of the hybrid entangled state toward the application of it. Here, we experimentally characterize the entanglement and quantum coherence of the prepared hybrid entangled state between a polarization-encoded discrete-variable qubit and a cat-encoded wave-like continuous-variable qubit. We show that the maximum quantum coherence is obtained when the probability of the horizontal-polarization photon is 0.5, and entanglement and quantum coherence of the hybrid entangled state are robust against loss in both discrete- and continuous-variable parts. Based on the experimentally reconstructed two-mode density matrix on the bases of polarization and cat state, we obtain the logarithm negativity of 0.57 and l1-norm of 0.82, respectively, which confirms the entanglement and quantum coherence of the state. Our work takes a crucial step toward the application of the polarization-cat hybrid entangled state.

Microscopes are indispensable tools in modern biology and medicine. With the development of microscopy, the signal-to-noise ratio of microscopes is now limited by the shot noise. Recently, quantum-enhanced microscopic imaging provides a feasible approach for improving the signal-to-noise ratio since it can beat the shot-noise limit by using quantum light. In this review, we first briefly introduce quantum states applied in quantum-enhanced microscopic imaging, and then we provide an overview of the principle and progress of quantum-enhanced stimulated Raman scattering microscopy, entangled two-photon microscopy, and quantum-enhanced differential interference contrast microscopy.

Orbital angular momentum (OAM) multiplexing provides an efficient method to improve data-carrying capacity in various quantum communication protocols. It is a precondition to distribute OAM multiplexed quantum resources in quantum channels for implementing quantum communication. However, quantum steering of OAM multiplexed optical fields and the effect of channel noise on OAM multiplexed quantum resources remain unclear. Here, we generate OAM multiplexed continuous-variable (CV) entangled states and distribute them in lossy or noisy channels. We show that the decoherence property of entanglement and quantum steering of the OAM multiplexed states carrying topological charges l=1 and l=2 are the same as that of the Gaussian mode with l=0 in lossy and noisy channels. The sudden death of entanglement and quantum steering of high-order OAM multiplexed states is observed in the presence of excess noise. Our results demonstrate the feasibility to realize high data-carrying capacity quantum information processing by utilizing OAM multiplexed CV entangled states.

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.