Almost Every Pure State of Three Qubits Is Completely Determined by Its Two-Particle Reduced Density Matrices

Abstract

In a system of $n$ quantum particles, we define a measure of the degree of irreducible $n$-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of $n-1$ particles. In the case of almost all pure states of three qubits, we show that there is no such correlation: almost every pure state of three qubits is completely determined by its two-particle reduced density matrices.