Quantum Correlations Beyond Entanglement

Abstract

A mixed state shared by two parties, Alice and Bob, is called classically correlated if it can be written as reported by Oppenheim (Physical Review Letters 89:180402, 2002) $\rho _\mathrm{{cc}}=\sum _{i,j}p_{ij}{\mathinner {|{i}\rangle }}{\mathinner {\langle {i}|}}^{A}\otimes {\mathinner {|{j}\rangle }}{\mathinner {\langle {j}|}}^{B},$ where $\{\mathinner {|{i}\rangle }^{A}\}$ are orthogonal states on Alice’s Hilbert space $\mathcal{H}_{A}$ and $\{\mathinner {|{j}\rangle }^{B}\}$ are orthogonal states on Bob’s Hilbert space $\mathcal{H}_{B}$.