Optimal quantum noise cancellation with an entangled witness channel

We present the digital signal processing of a mutually entangled, two-mode squeezed state using Wiener filtering to maximize the reduction of quantum noise of a single mode. By conditioning this mode, the signal, with its directly detected entangled pair, the witness, we show quantum noise cancellation of 2 dB below that of the signal vacuum level. We present the frequency-dependent digital recovery of squeezed states with Wiener filtering. This filtering is particularly relevant for gravitational wave detectors which will seek to use frequency-dependent squeezed states to improve their reach to the observable universe. We demonstrate the recovery of squeezed states in a configuration that replicates one which would provide optimum sensitivity improvement in a gravitational wave detector under the effects of radiation pressure noise. More generally, this technique may find application in other quantum-limited high-precision experiments such as those using optomechanical cavities.