Hadamard products of product operators and the design of gradient-diffusion experiments for simulating decoherence by NMR spectroscopy

An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations. (C) 2001 Elsevier Science B.V. All rights reserved.