Abstract

Specifying the quantum state of a system means providing its density matrix. Therefore, complete characterization of a system requires that its density matrix be determined in some representation. This is a difficult proposition because any detectable signal is related to the density matrix in such a way as to smooth out important features that can be attributed to quantum interference. In molecular emission tomography,¹ for example, this limits any reconstruction that uses the inverse radon transform to a positive-definite phase-space quasi-probability distribution from which it is difficult to retrieve the actual density matrix. To overcome the effects of this blurring, we have developed a new technique to directly reconstruct a quantum state density matrix in the number state representation. By incorporating the blurring effects of an experimental apparatus into the inversion algorithm, this technique provides direct access to the quantum state density matrix elements. While being relatively simple to implement in the laboratory, numerical simulations show this method to be robust enough to reconstruct a large variety of important quantum states.

© 1997 Optical Society of America