title: Crystallizing highly-likely subspaces that contain an unknown quantum state of light.
abstract: 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. In principle, the data themselves encode all information about the relevant subspace that physically contains the state. We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace by extracting this information directly from the data 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 assumptions about the source or preconceived parametric model subspaces are invoked. This ensures that no spurious reconstruction artifacts are present in state reconstruction as a result of inappropriate choices of the 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.
authors.affiliation: BK21 Frontier Physics Research Division, Seoul National University, 1 Gwanak-ro, Gwanak-gu, 08826 Seoul, South Korea.|Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.
authors.forename: Yong Siah
authors.initials: YS
authors.lastname: Teo
authors.affiliation: Institute of Physics, Belarus National Academy of Sciences, F. Skarina Ave. 68, 220072 Minsk, Belarus.
authors.forename: Dmitri
authors.initials: D
authors.lastname: Mogilevtsev
authors.affiliation: Institute of Physics, Belarus National Academy of Sciences, F. Skarina Ave. 68, 220072 Minsk, Belarus.
authors.forename: Alexander
authors.initials: A
authors.lastname: Mikhalychev
authors.affiliation: Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.
authors.forename: Jaroslav
authors.initials: J
authors.lastname: Řeháček
authors.affiliation: Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.
authors.forename: Zdeněk
authors.initials: Z
authors.lastname: Hradil