  We introduce and define a set of functions on pure bipartite states called
entanglement moments. Usual entanglement measures tell you if two systems are
entangled, while entanglement moments tell you both if and how two systems are
entangled. They are defined with respect to a measurement basis in one system
(e.g., a measuring device), and output numbers describing how a system (e.g., a
qubit) is entangled with that measurement basis. The moments utilize different
distance measures on the Hilbert space of the measured system, and can be
generalized to any N-dimensional Hilbert space. As an application, they can
distinguish between projective and non-projective measurements. As a particular
example, we take the Rabi model's eigenstates and calculate the entanglement
moments as well as the full distribution of entanglement.
