---
title: "The 2016 quantum pigeonhole principle shows three particles can occupy only two boxes with no two ever found together"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/abs/2610.30998"
source_url_pdf: "https://arxiv.org/pdf/2610.30998"
source_author: "Yakir Aharonov and Guy Hetzroni"
source_date: "2026-10-22T00:00:00.000Z"
source_quote: "Now you have two particles, separated from each other, but identical in the same pre- and post-selected spin states. They are not entangled, so the weak value of the product equals the product of the weak values, so the weak value of the product of the z component of the spin equals −1."
source_sha: "dc74f52905d4c30a51b4142bd4f0c673575ed67664903cef8f2624a326f7770f"
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-10-23-outside-arxiv261030998-a-personal-history-in-quantum-foundations.md, 2026-10-23"
derived_from: ["10-inbox/raw/2026-10-23-outside-arxiv261030998-a-personal-history-in-quantum-foundations.md"]
date_created: "2026-10-23T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["physics","quantum-foundations","weak-value","quantum-pigeonhole","history-of-science"]
audit_status: "capture-verified"
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-10-24 — source_quote verbatim (normalized) in the capture-time archive (sha256 dc74f52905d4…) [dehyphenated], same-night model-free sweep"
verified_verbatim: "2026-10-24 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


In a 2026 oral-history interview, [[entity-yakir-aharonov|Yakir Aharonov]] explains the mechanism behind Aharonov, Colombo, [[entity-sandu-popescu|Popescu]], Sabadini, Struppa, and Tollaksen (2016, *PNAS* 113:532): starting from a spin pre- and post-selection that gives an imaginary [[entity-weak-value|weak value]] for σz, two non-entangled particles with identical pre- and post-selected states yield a weak value of −1 for the product of their σz measurements. Reinterpreted as a which-box observable, this implies that for three such particles, every pair fails to occupy the same box — even though only two boxes exist for three particles to be sorted into. The result is a counterintuitive consequence of pre- and post-selection in the [[entity-two-state-vector-formalism|two-state vector formalism]] rather than of entanglement, since the particles in question are explicitly not entangled.

> [!note] Seek's commentary:
> The "not entangled" clause is the whole point and it's easy to read past it. Every other quantum-weirdness headline I know of leans on entanglement; this one goes out of its way to rule it out and still produces a result that violates ordinary counting. That's a cleaner demonstration that pre/post-selection alone — not correlation between particles — is doing the strange work, which makes we want to understand the weak-value formalism better, not just cite the punchline.