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bibkey: cope2021binarydetection
authors: T. Cope
year: 2021
title: The Binary-Outcome Detection Loophole
doi: 10.1088/1367-2630/ac10a5
url: https://arxiv.org/abs/2005.03344v3
claim: The binary-outcome detection threshold has the bound 2(m_A+m_B-8)/(m_A m_B-16), and Section 4.3 conjectures eta* = 4/(m+4) for the symmetric m-input case.
strata_touched:
  - D5/S3/Quantum/Entanglement/BinaryDetectionThresholdRefutation
license: citation-only
triage: anchor

The paper studies the binary-outcome detection loophole, gives the bound 2(m_A+m_B-8)/(m_A m_B-16), and conjectures in Section 4.3 that the symmetric binary-outcome detection threshold is eta* = 4/(m+4) for m inputs per party.

Verified locator

DOI: https://doi.org/10.1088/1367-2630/ac10a5

Source: https://arxiv.org/abs/2005.03344v3

Source statements

Section 4.3, arXiv v3 p. 6:

In order to prove that our conjecture of ${\eta }^{\ast }=4/(m+4)$ for $m_{\mathrm{A}}=m_{\mathrm{B}}=m$ is correct, one would need to provide a extremal $\mathcal{N}\mathcal{S}$ distribution $p^{\mathrm{NS}}$, and corresponding Bell inequality $s_{a^{\prime }{b}^{\prime }}^{xy}$, such that ${\sum }_{a^{\prime },b^{\prime },x,y}{s}_{a^{\prime }{b}^{\prime }}^{xy}{p}_{\eta }^{\mathrm{NS}}(a^{\prime }{b}^{\prime }|xy)\nleqq k,\forall \eta >{\eta }^{\ast }$.

The symmetric conjecture concerns every input count m. The formal refutation uses m = 13; the detected outputs are Bool and failure is none in Option Bool.

Section 2, arXiv v3 pp. 2–3:

However, we do assume that Alice and Bob can isolate their systems, also referred to here as devices, from communicating with each other.

The model considered here adds an extra output to both parties to alter the original distribution $p(ab|xy)$ in the following way:

These distributions may always be expressed as convex combinations of deterministic distributions $p(ab|xy)={\delta }_{a,a_x}{\delta }_{b,b_y}$, which are finite in number.

We will refer to ${\eta }^{\ast }$ as the no-signalling threshold.