Entanglement information rate distortion of a quantum Gaussian source

Quantum distortion operator is introduced based on canonical operators. As the lower bound of quantum information rate distortion, the entanglement information rate distortion is achieved by Gaussian map for Gaussian source. The entanglement information rate-distortion function is calculated for one-mode Gaussian source, it is achieved by a nontrivial unitary transformation. The rate distortion is achievable at zero distortion point. In contrast to the distortion defined via fidelity, our definition of the distortion makes it possible to calculate the entanglement information rate-distortion function for Gaussian source.