bibkey: marton2023onebit authors: István Márton; Erika Bene; Péter Diviánszky; Tamás Vértesi year: 2023 title: “Beating one bit of communication with and without quantum pseudo-telepathy” doi: 10.48550/arXiv.2308.10771 url: https://arxiv.org/abs/2308.10771v1 claim: “Two parallel copies of the CGLMP_d game have one-bit classical bound 12 for d = 2, …, 10, and the authors conjecture this for every d >= 2; the truncations [CGLMP_d^{⊗2}]_s and [CGLMP_d^{⊗2}]_a have conjectured local bounds 7 and 4, verified up to d = 20.” strata_touched:

• D5/S3/Quantum/Information/DoubleCglmpOneBitBound license: citation-only triage: anchor

Beating one bit of communication with and without quantum pseudo-telepathy

I. Márton, E. Bene, P. Diviánszky and T. Vértesi, arXiv:2308.10771 (v1 2023-08-21, the only version); npj Quantum Information 10, 79 (2024). Subject: quant-ph.

The paper looks for Bell-type inequalities that local hidden variables cannot satisfy even when one bit of classical communication is allowed. A local behaviour is P(ab|xy) = ∫ q(λ) P_A(a|xλ) P_B(b|yλ) (eq. P_LHV); with one bit l = l(x, λ) from Alice to Bob, Bob’s response is P_B(b|y l λ) (eq. P_LHV1bit), and the largest value of a Bell expression over these models is the one-bit bound L1bit. With outputs 0, …, d − 1,

CGLMP_d = P(A₀ ≥ B₀) + P(A₀ ≤ B₁) + P(A₁ < B₀) + P(A₁ ≥ B₁) ≤ 3,

and two copies are played in parallel. The authors state:

The one-bit bound L1bit(CGLMP_d^{⊗2}) = 12 in the last column is verified by the branch-and-bound algorithm up to d = 10. We conjecture that this is the exact bound for any d ≥ 2.

For the truncations to the inputs {00, 01, 11} of both parties, and to {00, 01, 11} and {00, 11}, they give “the conjectured local bound” 7 (“which we verified up to d = 20”) and “the conjectured local bound L = 4, which we verified up to d = 20”.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2308.10771
• URL: https://arxiv.org/abs/2308.10771v1 (source of v1 retrieved 2026-09-29).
• Location: the section on notation for eqs. (P_LHV) and (P_LHV1bit); the section on CGLMP_d inequalities for eq. (cglmpineq), Table IV and the conjecture; the subsections on the truncated double CGLMP inequalities for the bounds 7 and 4.