Operational Detection of Entanglement via Quantum Designs

From an operational point of view, several new entanglement detection criteria are proposed using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria with more settings are exactly equivalent to the corresponding ones with the minimal number of settings, namely the symmetric informationally complete positive operator-valued measures (SIC POVMs). Fundamentally, this observation highlights the potentially unique role played by SIC POVMs in quantum information processing. Experimentally, this provides the minimal number of settings that one should choose for detecting entanglement. Furthermore, it is found that nonlinear criteria are not always better than linear ones for the task of entanglement detection.