bibkey: portoetal2024tradeoffnonlocalitycontextuality
authors: Lucas E. A. Porto, Gabriel Ruffolo, Rafael Rabelo, Marcelo Terra Cunha and Paweł Kurzyński
year: 2024
title: "Trade-off relations between Bell nonlocality and local Kochen–Specker contextuality in generalized Bell scenarios"
doi: 10.1088/1367-2630/ad7167
url: "https://arxiv.org/abs/2405.02964v2"
claim: "In generalized Bell scenarios where Alice has two dichotomic measurements and Bob an n-cycle contextuality setup, normalized generalized-Bell and noncontextuality inequalities satisfy S_GBell + S_NC <= 1 on every nonsignaling and nondisturbing behavior for n = 3, 4, 5; the paper conjectures the same for every n."
strata_touched:
  - D5/S3/QuantumContext/NCycleNonlocalityContextualityTradeoff
license: citation-only
triage: anchor

Porto, Ruffolo, Rabelo, Terra Cunha and Kurzyński, Trade-off relations between Bell nonlocality and local Kochen–Specker contextuality in generalized Bell scenarios

L. E. A. Porto, G. Ruffolo, R. Rabelo, M. Terra Cunha and P. Kurzyński, New J. Phys. 26(8), 083028 (2024); arXiv:2405.02964v2. Quotations are from the v2 TeX source.

In a generalized Bell scenario Alice performs one of two dichotomic measurements $A_0,A_1$ and Bob one context $\{B_i,B_{i+1}\}$ (indices mod $n$) of an $n$-cycle of dichotomic measurements. Behaviors $p_{x,C_B}(a,\mathbf{b})$ that are nonsignaling and nondisturbing form the $\mathcal{N}\mathcal{S}\mathcal{ND}$ polytope; generalized-local behaviors are mixtures ${\sum }_{\lambda }q(\lambda )p_x^{\lambda }(a)p_{C_B}^{\lambda }(\mathbf{b})$ with nondisturbing Bob responses. An inequality $S$ is normalized when $S\le 0$ on local (respectively noncontextual) behaviors and its maximum over $\mathcal{N}\mathcal{S}\mathcal{ND}$ is $1$. Result 1 proves $S_{GBell}+S_{NC}\le 1$ on $\mathcal{N}\mathcal{S}\mathcal{ND}$ for $n=3,4,5$, and the paper states:

Consider a bipartite generalized Bell scenario where Bob has an $n$-cycle contextuality setup. For any normalized generalized-Bell inequality $S_{GBell}$ and any normalized noncontextuality inequality $S_{NC}$ of Bob’s local experiment, every $\mathcal{N}\mathcal{S}\mathcal{ND}$ behavior satisfies expression (12).

Verified locator

Source: https://arxiv.org/abs/2405.02964v2

• DOI: https://doi.org/10.1088/1367-2630/ad7167 (New Journal of Physics 26(8), 083028, 2024; title, authors, journal, volume and issue from Crossref).
• URL: https://arxiv.org/abs/2405.02964v2. The e-print member final_version.tex has 625 lines and md5 7b93583e359377061bc3289b38eedc53. Locations:
  • generalized Bell scenarios and the $\mathcal{N}\mathcal{S}\mathcal{ND}$ conditions, l. 181–196;
  • generalized locality, l. 213–219;
  • the $n$-cycle setup, l. 225;
  • normalization, l. 276;
  • Result 1, l. 279–286;
  • the conjecture, l. 373–375.