Detecting Correlated State-Preparation and Measurement Device Errors with Non-Holonomic Quantum Tomography

In standard quantum state tomography one prepares copies of an unknown state, subjects them to a complete set of controlled measurements, records the outcome probabilities, and performs some inversion of the Born rule to determine the state. Similarly, one can characterize an unknown detector with a complete set of known states. I consider the situation where one has both state-preparation and measurement devices with various settings, but none of which are characterized. By the Born rule, recording statistics alone cannot determine the states being prepared or the measurements made. Amazingly however, one can still determine if the settings between these devices produce states and measurements with correlated errors. [PRA 92(4), 042312] The technique has many formal similarities to classical thermodynamics as well as to gauge theory. [PRA 95(5), 052328]