Complete State Reconstruction of a Two-Mode Gaussian State via Local Operations and Classical Communication

We propose a strictly local quantum tomography protocol for a bipartite system. We show that the joint density matrix of an arbitrary two-mode Gaussian state, entangled or not, is obtained via local operations and classical communication only. In contrast to previous proposals, simultaneous homodyne measurements (HM) on both modes are replaced by local homodyne detections and a set of local projective measurements.