Pure state tomography with Pauli observables

Pure-state tomography requires expectation values on the order of the system’s dimension, a quadratic improvement compared to general tomography. We seek to understand the number of expectation values necessary to uniquely determine all pure states, with the additional restriction that we consider only the expectation values of Pauli observables. Applying results from classical computer science, we reduce this question to an instance of the hypergraph dualization problem, yielding a conjectured upper bound on the necessary number of expectation values. Our conjecture is conditioned on further understanding the possible linear combinations of Pauli observables.

This is ongoing, joint work with Jianxin Chen and Amir Kalev. Part of this work was supported by an NSF REU while an undergraduate intern at QuICS.