  A model of the Einstein-Bohr double-slit experiment is formulated in a fully
quantum theoretical setting. In this model, the state and dynamics of a movable
wall that has the double slits in it, as well as the state of a particle
incoming to the double slits, are described by quantum mechanics. Using this
model, we analyzed complementarity between exhibiting the interference pattern
and distinguishing the particle path. Comparing the Kennard-Robertson type and
the Ozawa-type uncertainty relations, we conclude that the uncertainty relation
involved in the double-slit experiment is not the Ozawa-type uncertainty
relation but the Kennard-type uncertainty relation of the position and the
momentum of the double-slit wall. A possible experiment to test the
complementarity relation is suggested. It is also argued that various phenomena
which occur at the interface of a quantum system and a classical system,
including distinguishability, interference, decoherence, quantum eraser, and
weak value, can be understood as aspects of entanglement.
