Tomography via Correlation of Noisy Measurement Records

We present methods and results of shot-by-shot correlation of noisy measurements to extract entangled state and process tomography in a superconducting qubit architecture \footnote{Ryan et al. arXiv:1310.6448 (2013)}. We show that averaging continuous values, rather than counting discrete thresholded values, is a valid tomographic strategy and is in fact the better choice in the low signal-to-noise regime. We show that the effort to measure $N$-body correlations from individual measurements scales exponentially with $N$, but with sufficient signal-to-noise the approach remains viable for few-body correlations. We provide a new protocol to optimally account for the transient behavior of pulsed measurements. Despite single-shot measurement fidelity that is less than perfect, we demonstrate appropriate processing to extract and verify entangled states and processes.