  Collapse of the wave function appears to violate the quantum superposition
principle as well as deterministic evolution. Objective collapse models propose
a dynamical explanation for this phenomenon, by making a stochastic non-unitary
and norm-preserving modification to the Schr\"odinger equation. In the present
article we ask how a quantum system evolves under a {\it deterministic} and
non-unitary but norm-preserving evolution? We show using a simple two-qubit
model that under suitable conditions, quantum linear superposition is broken,
with the system predictably driven to one or the other alternatives. If this
deterministic dynamics is coarse-grained and observed over a lower time
resolution, the outcomes appear random while obeying the Born probability rule.
Our analysis hence throws light on the distinct roles of non-unitarity and of
stochasticity in objective collapse models.
