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