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

TL;DR

This paper investigates the unique informational properties of generalized n-qubit GHZ states, showing they are the only pure states not fully determined by their (n-1)-qubit reduced states, highlighting their special role in quantum information.

Contribution

It identifies the unique status of generalized GHZ states as the only pure n-qubit states not determined by their reduced density matrices, emphasizing their exceptional informational characteristics.

Findings

Generalized GHZ states are not uniquely determined by (n-1)-qubit reductions.

They are the only pure states with this property among n-qubit states.

This highlights their special role in quantum information theory.

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.