  We identify subsystem fluctuations (variances) that measure entanglement in
an arbitrary bipartite pure state. These fluctuations are of observables that
generalize the notion of polarization to an arbitrary N-level subsystem. We
express this polarization fluctuation in terms of subsystem purity and other
entanglement measures. The derived fluctuation-entanglement relation is
evaluated for the ground states of a one-dimensional free fermion gas and the
Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for
experimentally measuring entanglement using Stern-Gerlach-type state selectors.
