Richard Kueng - Johannes Kepler University Extracting important information from a quantum system as efficiently and tractably as possible is an important subroutine in most quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties. The required number of measurements is independent of the system size and saturates information-theoretic lower bounds. Classical shadows also decompose nicely into elementary tensor products which facilitates storage and subsequent data processing. This is joint work with Robert Huang and John Preskill (both Caltech).