  We present a general theory of quantum information processing devices, that
can be applied to human decision makers, to atomic multimode registers, or to
molecular high-spin registers. Our quantum decision theory is a generalization
of the quantum theory of measurement, endowed with an action ring, a prospect
lattice and a probability operator measure. The algebra of probability
operators plays the role of the algebra of local observables. Because of the
composite nature of prospects and of the entangling properties of the
probability operators, quantum interference terms appear, which make actions
noncommutative and the prospect probabilities non-additive. The theory provides
the basis for explaining a variety of paradoxes typical of the application of
classical utility theory to real human decision making. The principal advantage
of our approach is that it is formulated as a self-consistent mathematical
theory, which allows us to explain not just one effect but actually all known
paradoxes in human decision making. Being general, the approach can serve as a
tool for characterizing quantum information processing by means of atomic,
molecular, and condensed-matter systems.
