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Indistinguishable particles have the same intrinsic particle properties, so exchanging their particle labels does not identify a different observable arrangement. Two electrons are an example; an electron and a proton belong to different species. Labels used as slots in a wavefunction are mathematical coordinates, not permanent identity tags.

For ordinary identical particles in three spatial dimensions, the symmetrization postulate takes the total quantum state to be symmetric for bosons or antisymmetric for fermions. In the antisymmetric case, exchanging all one-particle variables changes the sign of the wavefunction while leaving detection probabilities unchanged. The symmetry includes spin and other internal coordinates, not just position.

Spatial modes can nevertheless be addressed separately. Measuring the spin in one localized mode differs from measuring an imagined permanently labelled electron. Conditional spin measurement of identical fermions makes that distinction explicit. In two spatial dimensions, anyons allow more general exchange behavior; the boson/fermion alternative is not an unrestricted statement about every dimension.

For a conditional spin measurement of identical fermions addressing the $z$ component in one spatial mode, the Born rule givesConditioned on this result, the mode spin state is $|{\uparrow }_a{\downarrow }_b⟩$; the other outcome produces $|{\downarrow }_a{\uparrow }_b⟩$. The spin product is not a spin-exchange eigenstate. The measurement has selected an addressed mode and recorded an outcome, so this conditional spin description distinguishes the measured subsystem.

The full electron wavefunction still obeys fermionic exchange symmetry. For example, the conditional spin-up outcome in spatial mode $a$ is represented in particle coordinates byIt is antisymmetric under full particle exchange. Thus the loss of a definite symmetry of the conditional spin product does not mean that measurement turns identical electrons into distinguishable particles. If the outcome is discarded, the mode spin state is instead the equal mixture of the two opposite-spin products. The measurement must specify which spatial mode is addressed for the conditional statement to be operationally meaningful.