A measurement scheme for purity based on two two-body gates
  A scheme for measuring the purity of a quantum system with a finite number of levels is presented. The method makes use of two square root of SWAP gates and only hinges on measurements performed on a reference system, prepared in a certain pure state and coupled with the target system. Neither tomographic methods, with the complete reconstruction of the state, nor interferometric setups is needed. 
Hiromichi Nakazato, Toru Tanaka, Kazuya Yuasa, Giuseppe Florio,   Saverio Pascazio
quant-ph