Quantum Information Processing with Finite-State Information Transducers*

A quantum information source with a finite-state memory emits sequences of qudits that can be classically-correlated or entangled. These sequences are characterized by properties such as the von Neumann entropy rate and quantum excess entropy, calculated via the convergence of qudit block entropy to its asymptotic form. These quantities also serve as bounds on the classical information properties of observed sequences when using fixed-basis measurements. We show that qudit sequences serve as information reservoirs for quantum transducers that perform information-processing tasks and determine associated thermodynamic costs for operations such as erasure and synchronizing to the internal state of a given source via an adaptive measurement protocol.