Non-holonomic tomography and detecting state-preparation and measurement correlated errors

Quantum tomography is an important tool for characterizing the parameters of unknown states, measurements, and gates.  Standard quantum tomography is the practice of estimating these parameters with known measurements, states, or both, respectively.  In recent years, it has become important to address the issue of working with systems where the ``devices'' used to prepare states and make measurements both have significant errors.  Of particular concern to me is whether such state-preparation and measurement errors are correlated with each other.  In this talk, I will share a solution to assessing such correlations with an object called a partial determinant.  Further, I will show how this technique suggests a perspective for such correlated quantum states and observables (over the space of device settings) is analogous to the non-holonomic perspectives of thermodynamic heat and work (over the macroscopic state space.)