  We introduce two families of criteria for detecting and quantifying the
entanglement of a bipartite quantum state of arbitrary local dimension. The
first is based on measurements in mutually unbiased bases and the second is
based on equiangular measurements. Both criteria give a qualitative result in
terms of the state's entanglement dimension and a quantitative result in terms
of its fidelity with the maximally entangled state. The criteria are
universally applicable since no assumptions on the state are required.
Moreover, the experimenter can control the trade-off between
resource-efficiency and noise-tolerance by selecting the number of measurements
performed. For paradigmatic noise models, we show that only a small number of
measurements are necessary to achieve nearly-optimal detection in any
dimension. The number of global product projections scales only linearly in the
local dimension, thus paving the way for detection and quantification of very
high-dimensional entanglement.
