Abstract
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.
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