States of a multiparticle quantum system are useful for quantum information processing when they are entangled, i.e., not product states relative to the tensor product decomposition of the Hilbert space corresponding to the particles. Arbitrary entanglements between parts of a quantum system are not possible, however; they must satisfy certain “monogamy” constraints which limit how much multiple different subsystems can be entangled with one another. The standard monogamy constraints can be generalized in several ways: in this talk we’ll tighten some, generalize others to higher dimensional tensor factors, and derive inequalities satisfied by symmetric sets of entanglement measures. Along the way we’ll contrast the quantum results with corresponding statements about classical random variables.

https://math.ucsd.edu/people/profiles/david-meyer/