Complexity of multivariate problems based on binary information

This note suggests some investigations about the complexity of multivariate problems based on quantized information rather than standard information. The extreme case of binary information is studied on two classical examples: the integration of multivariate Lipschitz functions, for which it is shown that adaptivity of the quantization process is beneficial, and the integration of multivariate trigonometric polynomials, for which it is hinted that special binary information is superior to standard binary information.