Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography

摘要

Whenever we do not have an informationally complete set of measurements, the estimate of a quantum statencannot be uniquely determined. In this case, among the density matrices compatible with the available data,nthe one commonly preferred is the one which is the most uncommitted to the missing information. This is thenpurpose of the maximum entropy estimation (MaxEnt) and the variational quantum tomography (VQT). Here,nwe propose a variant of VQT and show its relationship with MaxEnt methods in quantum tomographies withnan incomplete set of measurements. We prove their equivalence in the case of eigenbasis measurements, andnthrough numerical simulations we stress their similar behavior. Hence, in the modified VQT formulation we havenan estimate of a quantum state as unbiased as in MaxEnt and with the benefit that VQT can be more efficientlynsolved by means of linear semidefinite programs.