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Collective uncertainty in partially polarized and partially decohered spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:math>systems
It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum $J=\mathit{Nj}$, where $j$ is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble to the so-called symmetric Hilbert space. Here, we argue that symmetric states …