Verifying the Quantumness of Bipartite Correlations

Entanglement is at the heart of most quantum information tasks, and therefore considerable effort has been made to find methods of deciding the entanglement content of a given bipartite quantum state. Here, we prove a fundamental limitation to deciding if an unknown state is entangled or not: we show that any quantum measurement which can answer this question for an arbitrary state necessarily gives enough information to identify the state completely. We also extend our treatment to other classes of correlated states by considering the problem of deciding if a state has negative partial transpose, is discordant, or is fully classically correlated. Remarkably, only the question related to quantum discord can be answered without resorting to full state tomography.