  Consecutive quantum measurements performed on the same system can reveal
fundamental insights into quantum theory's causal structure, and probe
different aspects of the quantum measurement problem. According to the
Copenhagen interpretation, measurements affect the quantum system in such a way
that the quantum superposition collapses after the measurement, erasing any
knowledge of the prior state. We show that a sequence of measurements in a
collapse picture is equivalent to a quantum Markov chain, and that considering
the unitary evolution of quantum wavefunctions interacting consecutively with
more than two detectors reveals an experimentally measurable difference between
a collapse and unitary picture. The non-Markovian nature of sequential
measurements that we report is consistent with earlier discoveries in optimal
quantum state discrimination.
