  The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their
local unitary equivalents are the only states of n qubits that are not uniquely
determined among pure states by their reduced density matrices of n-1 qubits.
Thus, among pure states, the generalized GHZ states are the only ones
containing information at the n-party level. We point out a connection between
local unitary stabilizer subgroups and the property of being determined by
reduced density matrices.
