Almost non state-altering POVM quantum measurement - Advincula, Janus B.; Galapon, Eric A. (Quezon City Institute of Physics, College of Science, University of the Philippines Diliman, 2016)
The measurement process of a quantum system interacting with the measuring apparatus is properly described by positive operator-valued measures or POVM's. It provides the most general description of quantum measurement. In this thesis, we mathematically prove that, for invertible density matrices, there are no POVMs that leave the quantum state completely unaltered after measurement. Furthermore, for a given POVM and initial density matrix, there is a minimum amount of disturbance that a measurement imparts to the quantum state.This disturbance may be measured by the trace distance between the initial and final density matrices. Lastly, this trace distance is bounded below by the absolute value of the eigenvalue differences of the initial and final density matrices. We've also worked out the minimal state-altering POVM for two-level systems or qubits.
Thesis (M.S.-Applied Physics) --University of the Philippines Diliman
Keywords: Quantum systems; Operator-valued measures