Entanglement Detection Beyond Measuring Fidelities

Understand

One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state.

• In this Letter we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful.
• We find that unfaithful states are ubiquitous in information theory.
• For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful.