  In presence of dissipation, quantal states may acquire complex-valued phase
effects. We suggest a notion of dissipative interferometry that accommodates
this complex-valued structure and that may serve as a tool for analyzing the
effect of certain kinds of external influences on quantal interference. The
concept of mixed-state phase and concomitant gauge invariance is extended to
dissipative internal motion. The resulting complex-valued mixed-state
interference effects lead to well-known results in the unitary limit and in the
case of dissipative motion of pure quantal states. Dissipative interferometry
is applied to fault-tolerant geometric quantum computation.
