  Quantum optical Gaussian states are a type of important robust quantum states
which are manipulatable by the existing technologies. So far, most of the
important quantum information experiments are done with such states, including
bright Gaussian light and weak Gaussian light. Extending the existing results
of quantum information with discrete quantum states to the case of continuous
variable quantum states is an interesting theoretical job. The quantum Gaussian
states play a central role in such a case. We review the properties and
applications of Gaussian states in quantum information with emphasis on the
fundamental concepts, the calculation techniques and the effects of
imperfections of the real-life experimental setups.
  Topics here include the elementary properties of Gaussian states and relevant
quantum information device, entanglement-based quantum tasks such as quantum
teleportation, quantum cryptography with weak and strong Gaussian states and
the quantum channel capacity, mathematical theory of quantum entanglement and
state estimation for Gaussian states.
