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We show that any sequence of measurements on a permutationally-symmetric(pure or mixed) multi-qubit string leaves the unmeasured qubit substring alsopermutationally-symmetric. In addition, we show that the measurementprobabilities for an arbitrary sequence of single-qubit measurements areindependent of how many unmeasured qubits have been lost prior to themeasurement. Our results are valuable for quantum information processing ofindistinguishable particles by post-selection, e.g. in cases where the resultsof an experiment are discarded conditioned upon the occurrence of a given eventsuch as particle loss. Furthermore, our results are important for the design ofadaptive-measurement strategies, e.g. a series of measurements where for eachmeasurement instance, the measurement basis is chosen depending on priormeasurement results.

Ordered Measurements of Permutationally-Symmetric Qubit Strings