On the Simplest Entangled Mixed States

Quantum entanglement is a fascinating topic with both theoretical and technological impacts. Yet, even in the simplest scenarios, there are still various open questions involving pure state and mixed state entanglement. Here we present the simplest entangled mixed states. We consider both qubits (quantum bits) and qudits (quantum digits). We first provide our simplest yet most important result for rank-2 bi-partite states, and we then generalize our results to go beyond rank-2 and to go beyond bi-partite states.