Ordered Measurements of Permutationally-Symmetric Qubit Strings

TL;DR

This paper demonstrates that measurements on permutationally-symmetric multi-qubit strings preserve symmetry and that measurement probabilities are unaffected by prior particle loss, aiding quantum information processing and adaptive strategies.

Contribution

It establishes that permutational symmetry is maintained under measurements and that measurement probabilities are independent of prior qubit loss, advancing quantum measurement techniques.

Findings

Permutational symmetry is preserved after measurements.

Measurement probabilities are unaffected by prior particle loss.

Results facilitate quantum information processing with indistinguishable particles.

Abstract

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.