Toward an expected utility theory of entanglement: Optimization of a probabilistic entanglement protocol

A utility theory of entanglement is formulated, based on the von Neumann--Morgenstern theorem. As a specific example, a protocol for measurement--induced entanglement is studied, in which the amount of entanglement obtained depends on the random result of a measurement on an ancilla. It is shown that the maximization of the utility requires a non--trivial strategy. The results are especially useful when the interaction between the ancilla and the systems to be entangled is weak.