The Parts Determine the Whole except for n-Qubit Greenberger-Horne-Zeilinger States

Abstract

The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their local unitary equivalents are the only pure states of n qubits that are not uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices of n-1 qubits. Thus, the generalized GHZ states are the only ones containing information at the n-party level.