Quantum Subspace Measurements

Fundamental studies of quantum measurements and their capacity to acquire information are typically based on scenarios in which the full Hilbert space of the measured quantum system is open to measurement interactions. In this work, we consider a class of incomplete quantum measurements – quantum subspace measurements (QSM’s) – for which all measurement interactions are restricted to an arbitrary but specified subspace of the measured system Hilbert space. We define QSM’s formally through a condition on the measurement Hamiltonian, obtain forms for the post-measurement states and positive operators (POVM elements) associated with QSM’s acting in a specified subspace, and upper bound the accessible information for such measurements. Characteristic features of QSM’s are identified and discussed.