Quantum State Tomography with Tight Signed Measurement Frames with Applications for Fermionic Tomography

Frame theory provides an elegant means for reconstructing vector spaces using overcomplete sets of vectors via dual frames. These can be generalized to measurement frames for quantum systems, and have recently been shown to have a close connection with classical shadows. A tight informationally complete positive operator valued measure (or, tight IC-POVM) represents an optimal quantum measurement frame for generic state tomography. In this talk, we look at generalizations of tight IC-POVMs using signed measures. These allow for the flexible generation of measurement frames that are easily invertible and can be realized via additional measurement costs. Importantly, we introduce a construction with applications for fermionic tomography and quantum simulation with a constant scaling measurement overhead and a linear number of entangling gates.