Probing the structure of entanglement with entanglement moments

•We introduce entanglement moments to tell how a system is entangled.•Evaluation is presented for an S1 subset of the Hilbert space, S2, and CPnCPn.•Examples are provided to illustrate what is being measured.•A working example of the Rabi model׳s eigenstates is presented.

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.