bibkey: tavakolizambrinicruzeirouolaabbott2021contextual
authors: Armin Tavakoli; Emmanuel Zambrini Cruzeiro; Roope Uola; Alastair A. Abbott
year: 2021
title: "Bounding and simulating contextual correlations in quantum theory"
doi: 10.1103/PRXQuantum.2.020334
url: "https://arxiv.org/abs/2010.04751v3"
claim: "The paper introduces a hierarchy of semidefinite relaxations that bounds quantum correlations in prepare-and-measure contextuality scenarios, applies it to several noncontextuality inequalities, and conjectures from a numerical bound that quantum models with pure preparations cannot violate the Hameedi-Tavakoli-Marques-Bourennane inequality."
strata_touched:
  - D5/S3/Quantum/Contextuality/PureStateHTMBBound
license: citation-only
triage: anchor

Tavakoli, Zambrini Cruzeiro, Uola and Abbott, Bounding and simulating contextual correlations in quantum theory

A. Tavakoli, E. Zambrini Cruzeiro, R. Uola and A. A. Abbott, PRX Quantum 2(2) (2021) 020334, DOI 10.1103/PRXQuantum.2.020334; arXiv:2010.04751v3. Quotations are from the arXiv v3 TeX source.

In the Hameedi-Tavakoli-Marques-Bourennane (HTMB) scenario Alice receives two trits $x=x_1{x}_2$ and prepares ${\rho }_x$, and Bob receives $y\in \{1,2\}$ and outputs a trit $b$. The operational equivalences say that Alice sends no information about $x_1+x_2$ and about $x_1+2x_2$ modulo $3$. The HTMB inequality is ${\mathcal{A}}_{\mathrm{HTMB}}=\frac{1}{18}{\sum }_{x,y}p(b=x_y\mid x,y)\le \frac{2}{3}$. After bounding ${\mathcal{A}}_{\mathrm{HTMB}}$ over models with pure preparations by $\lesssim 0.667$, the paper writes:

This gives us strong evidence (i.e., up to numerical precision) that pure states cannot violate the HTMB inequality~\eqref{eq:HTMB}, and we conjecture this to indeed be the case exactly.

Verified locator

Source: https://arxiv.org/abs/2010.04751v3

• DOI: https://doi.org/10.1103/PRXQuantum.2.020334 (journal version; title, authors, journal, volume, issue and article number from Crossref; the journal text was not read).
• URL: https://arxiv.org/abs/2010.04751v3. The e-print member Manuscript_infocontext_reresubmission.tex has 1100 lines and md5 f767464510150f9e02bc504393cf40e8. Locations:
  • the HTMB scenario, its operational equivalences and the inequality, l. 492–499;
  • the pure-state bound and the conjecture, l. 502–506;
  • the mixed-state violation in dimension six, l. 508.