On-chip continuous-variable quantum entanglement

Entanglement is an essential feature of quantum theory and the core of the majority of quantum information science and technologies. Quantum computing is one of the most important fruits of quantum entanglement and requires not only a bipartite entangled state but also more complicated multipartite entanglement. In previous experimental works to demonstrate various entanglement-based quantum information processing, light has been extensively used. Experiments utilizing such a complicated state need highly complex optical circuits to propagate optical beams and a high level of spatial interference between different light beams to generate quantum entanglement or to efficiently perform balanced homodyne measurement. Current experiments have been performed in conventional free-space optics with large numbers of optical components and a relatively large-sized optical setup. Therefore, they are limited in stability and scalability. Integrated photonics offer new tools and additional capabilities for manipulating light in quantum information technology. Owing to integrated waveguide circuits, it is possible to stabilize and miniaturize complex optical circuits and achieve high interference of light beams. The integrated circuits have been firstly developed for discrete-variable systems and then applied to continuous-variable systems. In this article, we review the currently developed scheme for generation and verification of continuous-variable quantum entanglement such as Einstein-Podolsky-Rosen beams using a photonic chip where waveguide circuits are integrated. This includes balanced homodyne measurement of a squeezed state of light. As a simple example, we also review an experiment for generating discrete-variable quantum entanglement using integrated waveguide circuits.