Repeated quantum non-demolition measurements

 We describe, in detail, theoretical and experimental aspects related to our recently reported repeated back-action evading measurements performed using two travelling-wave optical parametric amplifiers in series. The state of the observable being measured is almost perfectly preserved after two successive measurements. The final signal, and the intermediate measurement of the two successive setups are quantum correlated with conditional variances that lie in the quantum regime. Moreover, we show that the two independent measurements are quantum correlated up to 30%.