  The decay of a parent particle into two or more daughter particles results in
an entangled quantum state as a consequence of conservation laws in the decay
process. Recent experiments at Belle and BaBar take advantage of quantum
entanglement and the correlations in the time evolution of the product
particles to study CP and T violations. If one (or more) of the product
particles are not observed, their degrees of freedom are traced out of the pure
state density matrix resulting from the decay, leading to a mixed state density
matrix and an entanglement entropy. This entropy is a measure of the loss of
information present in the original quantum correlations of the entangled
state. We use the Wigner-Weisskopf method to construct an approximation to this
state that evolves in time in a {\em manifestly unitary} way. We then obtain
the entanglement entropy from the reduced density matrix of one of the daughter
particles obtained by tracing out the unobserved states, and follow its time
evolution. We find that it grows over a time scale determined by the lifetime
of the parent particle to a maximum, which when the width of the parent
particle is narrow, describes the phase space distribution of maximally
entangled Bell-like states. The method is generalized to the case in which the
parent particle is described by a wave packet localized in space. Possible
experimental avenues to measure the entanglement entropy in the decay of mesons
at rest are discussed.
