We show that any sequence of measurements on a permutationally-symmetric
(pure or mixed) multi-qubit string leaves the unmeasured qubit substring also
permutationally-symmetric. In addition, we show that the measurement
probabilities for an arbitrary sequence of single-qubit measurements are
independent of how many unmeasured qubits have been lost prior to the
measurement. Our results are valuable for quantum information processing of
indistinguishable particles by post-selection, e.g. in cases where the results
of an experiment are discarded conditioned upon the occurrence of a given event
such as particle loss. Furthermore, our results are important for the design of
adaptive-measurement strategies, e.g. a series of measurements where for each
measurement instance, the measurement basis is chosen depending on prior
measurement results.Comment: 13 page