Compressed Sensing

The steady growing number of quantum bits used in modern quantum information experiments gives rise to new problems. Especially if we want to determine the quantum state used in an experiment, i.e. ascertain the density matrix of the state, the number of needed measurement settings scales exponentially bad with Θ(4n), where n is the number of qubits. Compressed sensing is a technique developed to overcome this problem by using matrix completion methods to reconstruct a full density matrix of low rank states with fewer measurements. This report explains themain ideas of compressed sensing to the reader and gives a (highly incomplete) overview of the work done in the field. It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out. E. Artin