Continuous decomposition of quantum measurements via Hamiltonian feedback

Center for Quantum Information Science and Technology,Communication Sciences Institute, Department of Electrical Engineering,University of Southern California Los Angeles, CA 90089, USA.(Dated: April 16, 2015)We characterize the set of generalized quantum measurements that can be decomposed into acontinuous measurement process using a stream of probe qubits and a tunable interaction Hamilto-nian. Each probe in the stream interacts weakly with the target quantum system, then is measuredprojectively in a standard basis. This measurement result is used in a closed feedback loop to tunethe interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process withthe structure of a one-dimensional random walk. To maintain this structure, and require that atlong times the measurement outcomes be independent of the path, the allowed interaction Hamil-tonians must lie in a restricted set, such that the Hamiltonian terms on the target system form a nite dimensional Jordan algebra. This algebraic structure of the interaction Hamiltonians yields alarge class of generalized measurements that can be continuously performed by our scheme, and wefully describe this set.