  From an operational point of view, we propose several new entanglement
detection criteria 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, we find that nonlinear criteria are not always better than linear
ones for the task of entanglement detection.
