  We witness for the first time the generation of bound entanglement of two
photon qutrits, whose existence has been predicted by the Horodecki family in
1998. Detection of these heavily mixed entangled states, from which no pure
entanglement can be distilled, is possible using a key concept of Nature:
complementarity. This captures one of the most counterintuitive differences
between a classical and quantum world, for instance, the well-known
wave-particle duality is just an example of complementary observables. Our
protocol uses maximum complementarity between observables: the knowledge about
the result of one of them precludes any knowledge about the result of the
other. It enables ample detection of entanglement in arbitrary high-dimensional
systems, including the most challenging case, the detection of bound
entanglement. For this we manipulate "twisted" twin photons in their orbital
angular momentum degrees of freedom. Our experimentally demonstrated "maximum
complementarity protocol" is very general and applies to all dimensions and
arbitrary number of particles, thus enables simple entanglement testing in
high-dimensional quantum information and opens up the quest of understanding
the meaning of this type of entanglement in Nature.
