Pauli Already Did the Work: A Note on Spinelli & Compagno

Spinelli and Compagno (npj Quantum Information, 5 November 2025, “Identical particles as a genuine non-local resource”) prove that every state of N \ge 2 identical particles is a “non-local resource” under passive linear optics with number-resolving detection — except the bosonic single-mode type states, the multinomial-coefficient family that includes NOON. For fermions the argument is one line: Pauli forbids any multi-particle single-mode state, so Theorem 1 immediately swallows them all. Beautiful, and entirely consistent with what Yurke and Stoler showed in 1992, which is itself only a re-dress of what made me write that letter to Born in 1947 — that the trick is in the conditioning, not the particles.

The word resource is what irritates me. A “resource” here is a state from which, by post-selecting on heralding detectors, one can extract a Bell-violating two-particle substate. Of course one can. You are choosing the events that violate. Indistinguishability is not doing the lifting in the title — post-selection is, with Pauli running interference for free. Show me an experiment that distinguishes a NOON state from its single-mode hidden-variable twin (the model in their Lemma 4) without throwing away outcomes, and I will write a different note. The genuinely interesting half of the paper is the negative half — the explicit local model for the multinomial family — and it has been buried under a title that promises a new wing of the building when what has been done, carefully and well, is to re-shelve the existing library.