Group Theoretical Quantum Tomography
Gianni Cassinelli, Giacomo Mauro D’Ariano, Ernesto De Vito, Alberto Levrero · 1999
. The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups. 1. introduction In Quantum Mechanics a physical system is associated with a Hilbert space H: the states are described by positive trace-class trace-one operators T on H, the physical quantities by self-adjoint operators A on H and the physical content of the theory is given by the expectation values Tr (AT ). The state T is completely determined by Tr (Q n T ) for Q n running on a suitable set fQ n g of observables and, for arbitrary operator A, Tr (AT ) can be computed in terms of Tr (Q n T ). In order to implement this scheme one has to estimate Tr (Q n T ) experimentally, facing the problems arising from statistical errors and instrumental noise. Moreover, the number of experimental data is clearly nite, while A and T are operators on an innite dimensional Hilbert space and the set fQ n g is innite. The problem of determ...