Reconstructing Gaussian bipartite states with a single polarization-sensitive homodyne detector

We present a novel method to fully estimate Gaussian bipartite polarization states using only a single homodyne detector. Our approach is based on [Phys. Rev. Lett.102, 020502 (2009)10.1103/PhysRevLett.102.020502], but circumvents additional optics, and thereby losses, in the signal path. We provide an intuitive explanation of our scheme without needing to define auxiliary modes. With six independent measurements, we fully reconstruct the state's covariance matrix. We validate our method by comparing it to a conventional dual-homodyne measurement scheme.