Expected Utility and the Density Matrix

This paper aims to analyze the effects of adding quantum mechanics to the expected utility problem. That is, how is an agent’s behavior regarding taking a gamble among many states of the world modified when those states fall in the framework of quantum mechanics? The paper restricts analysis to the two-state system for simplicity. Expected utility and the classical results are reviewed. Quantum mechanics and superposition are brought into the picture, followed by the introduction of more general classical-esque state mixtures through density matrices. Finally, the expansion of possibilities through the addition of quantum entanglement is discussed. This paper assumes moderate familiarity of the principles and formalism of single-particle quantum mechanics as well as an ability to pick up on basic understanding of density matrices, but does not assume too much familiarity with consumer choice theory.