6 Quantum Tomography from Incomplete Data via MaxEnt Principle

Abstract

We show how the maximum entropy (MaxEnt) principle can be efficiently used for a reconstruction of states of quantum systems from incomplete tomographic data. This MaxEnt reconstruction scheme can be in specific cases several orders of magnitude more efficient than the standard inverse Radon transformation or the reconstruction via direct sampling using pattern functions. We apply the MaxEnt algorithm for a reconstruction of motional quantum states of neutral atoms. As an example we analyze the experimental data obtained by the group of C. Salomon at the ENS in Paris and we reconstruct Wigner functions of motional quantum states of Cs atoms trapped in an optical lattice. We also reconstruct Wigner functions of a cavity field based on a measurement of the parity operator. We analyze in detail experimental data obtained by the group of S. Haroche at the ENS in Paris.