Tomography via correlation of noisy measurement records

We present methods and results for tomographic measurement of quantum systems through shot-by-shot correlation of individual qubit measurements. Rather than inferring the qubit state after each measurement, we show that averaging of continuous soft values is a valid tomographic strategy and is in fact the better choice in the regime of low signal-to-noise ratio. We experimentally demonstrate a matched filter approach to account for a transient measurement response, and use this to show that tomography of entangled states is feasible despite the asymptotic exponential effort required to obtain N-body corrleations.