Crystallizing highly-likely subspaces that contain an unknown quantum   state of light
  In continuous-variable tomography, with finite data and limited computation resources, reconstruction of a quantum state of light is performed on a finite-dimensional subspace. No systematic method was ever developed to assign such a reconstruction subspace---only ad hoc methods that rely on hard-to-certify assumptions about the source and strategies. We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace for any given unknown quantum state of light and measurement scheme. This procedure makes use of the celebrated statistical principle of maximum likelihood, along with other validation tools, to grow an appropriate seed subspace into the optimal reconstruction subspace, much like the nucleation of a seed into a crystal. Apart from using the available measurement data, no other spurious assumptions about the source or ad hoc strategies are invoked. As a result, there will no longer be reconstruction artifacts present in state reconstruction, which is a usual consequence of a bad choice of reconstruction subspace. The procedure can be understood as the maximum-likelihood reconstruction for quantum subspaces, which is an analog to, and fully compatible with that for quantum states. 
Yong Siah Teo, Dmitri Mogilevtsev, Alexander Mikhalychev, Jaroslav   Rehacek, Zdenek Hradil
quant-ph