Entanglement Criteria for Continuous-Variable States

Entanglement is an amazing feature of quantum mechanics which is a nontrivial non-local correlation between states. It is studied and exploited greatly in the field of quantum information. Traditionally, most quantum systems of interest in quantum information is described by discrete variable states, e.g. spin of particles. Thus, entanglement is studied to a considerable extent in such state. Nevertheless, in practice, there are a number of quantum systems that must be described by continuous variable states such as electromagnetic fields in quantum optics. Thus, it is also important to understand entanglement in the context of continuous variable states. In particular, to be able to study entanglement properly, it is very necessary to find a method to identify whether a state is entangled or separable and to quantify how much entangled a state is. This report is a review of several criteria and measures used to deal with entanglement in both Gaussian and non-Gaussian continuous variable states, including some prelimary backgrounds.