  Quantum systems can display particle- or wave-like properties, depending on
the type of measurement that is performed on them. The Bell-state quantum
eraser is an experiment that brings the duality to the forefront, as a single
measurement can retroactively be made to measure particle-like or wave-like
properties (or anything in between). Here we develop a unitary
information-theoretic description of this (and several related) quantum
measurement situations that sheds light on the trade-off between the quantum
and classical features of the measurement. In particular, we show that both the
coherence of the quantum state and the classical information obtained from it
can be described using quantum-information-theoretic tools only, and that those
two measures satisfy an equality on account of the chain rule for entropies.
The coherence information and the which-path information have simple
interpretations in terms of state preparation and state determination, and
suggest ways to account for the relationship between the classical and the
quantum world.
