bibkey: kurzynski2017contextualityidentical
authors: Paweł Kurzyński
year: 2017
title: "Contextuality of identical particles"
doi: 10.1103/PhysRevA.95.012133
url: "https://arxiv.org/abs/1609.01250v1"
claim: "For N identical particles occupying the modes of the 18-projector Kochen–Specker set, a non-contextual model assigns occupation numbers to modes with each context summing to N; the paper shows state-dependent contextuality for every N>0, shows that no state-independent contextuality arises for N=2, and leaves open whether for some N>2 the bosonic occupation numbers cannot be assigned non-contextually."
strata_touched:
  - D5/S3/Quantum/Contextuality/EighteenModeBosonicAssignmentParity
license: citation-only
triage: anchor

Kurzyński, Contextuality of identical particles

P. Kurzyński, Phys. Rev. A 95(1), 012133 (2017); arXiv:1609.01250v1. Quotations are from the v1 TeX source.

A non-contextual hidden-variable model for $N$ identical particles occupying a family of modes assigns to each mode an occupation number, $v_B\in \{0,1,2,\dots \}$ for bosons and $v_F\in \{0,1\}$ for fermions, independently of the context, such that in every context (a set of mutually orthogonal modes resolving the identity) the occupation numbers sum to $N$. For the 18-projector Kochen–Specker set in dimension 4, the modes are labeled $v_{ij}$, where $i$ and $j$ are the two of the nine contexts containing the mode; for $N=1$ the paper derives a contradiction because the nine context sums total 9 while each mode is counted twice. It shows state-dependent contextuality for every $N>0$ and states:

However, the lack of the state-independent contextuality was only shown for $N=2$. It is possible that for some $N>2$ the bosonic occupation numbers of 18 modes cannot be assigned in a non-contextual way. This would require further research, since for large numbers of particles there are many ways in which the particles can be distributed between the modes.

Verified locator

Source: https://arxiv.org/abs/1609.01250v1

• DOI: https://doi.org/10.1103/PhysRevA.95.012133 (Physical Review A 95(1), 012133; title, author, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/1609.01250v1. The e-print member contextuality_fermions.tex has 319 lines and md5 79699ac68ef10a4972308aaa8c1d447b. Locations:
  • the occupation-assignment model and the conservation condition, Eq. (1), l. 74–81;
  • the 18-mode set, the labels $v_{ij}$ and the $N=1$ parity argument, l. 83;
  • the nine contexts, l. 132–221;
  • the open question for $N>2$ bosons, l. 233.