  Whenever we do not have an informationally complete set of measurements, the
estimate of a quantum state can not be uniquely determined. In this case, among
the density matrices compatible with the available data, it is commonly
preferred that one which is the most uncommitted with the missing information.
This is the purpose of the Maximum Entropy estimation (MaxEnt) and the
Variational Quantum Tomography (VQT). Here, we propose a variant of Variational
Quantum Tomography and show its relationship with Maximum Entropy methods in
quantum tomographies with incomplete set of measurements. We prove their
equivalence in case of eigenbasis measurements, and through numerical
simulations we stress their similar behavior. Hence, in the modified VQT
formulation we have an estimate of a quantum state as unbiased as in MaxEnt and
with the benefit that VQT can be more efficiently solved by means of linear
semidefinite programs.
