bibkey: tavakoliabbottrenougisinbrunner2018sdi
authors: Armin Tavakoli, Alastair A. Abbott, Marc-Olivier Renou, Nicolas Gisin and Nicolas Brunner
year: 2018
title: "Semi-device-independent characterization of multipartite entanglement of states and measurements"
doi: 10.1103/PhysRevA.98.052333
url: https://arxiv.org/abs/1805.00377v1
claim: "In the semi-device-independent prepare-and-measure game with n parties of local dimension d, a measurement with at least k fully separable operators has success probability at most d^{-n}(d^n − k + k/d); for n = 2 the bound is attained with k = md separable operators for every m, and the paper leaves open whether a similar partial tightness holds for general n."
strata_touched:
  - D5/S3/Quantum/Measurement/MultipartiteEntangledMeasurementPartialTightness
license: citation-only
triage: anchor

Tavakoli–Abbott–Renou–Gisin–Brunner, semi-device-independent characterization of multipartite entanglement

A. Tavakoli, A. A. Abbott, M.-O. Renou, N. Gisin and N. Brunner, Phys. Rev. A 98, 052333 (2018); arXiv:1805.00377v1 (arXiv title “Semi-device-independent characterisation of multipartite entangled states and measurements”). Quotations are from the v1 TeX source.

Parties $A_1,\dots ,A_n$ apply transformations ${\mathcal{T}}_{x_k{y}_k}^{(k)}$ to a shared state $\rho$ of local dimension $d$, and $B$ measures $\{M_{\mathbf{b}}\}$; the figure of merit ${\mathcal{A}}_{n,d}$ averages the probability of the winning string $C(\mathbf{x},\mathbf{y})$ with $b_1={\sum }_i{x}_i$ and $b_k=y_k-y_1$ modulo $d$. An operator is fully separable if it is a positive combination of positive product operators. Result 2 bounds ${\mathcal{A}}_{n,d}\le d^{-n}(d^n-k+k/d)$ for a measurement with at least $k$ fully separable operators. For $n=2$, Appendix C attains the bound with $k=md$ and states:

We leave it as an open question whether a similar partial tightness result holds in the more general $n$ partite case.

Verified locator

Source: https://arxiv.org/abs/1805.00377v1

• DOI: https://doi.org/10.1103/PhysRevA.98.052333 (Physical Review A 98(5), article 052333; title, authors, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/1805.00377v1. The e-print member SDI_manuscript.tex has 501 lines and md5 1888cb2a743d8cbcda8d1f130274799b. Locations:
  • the scenario and ${\mathcal{A}}_{n,d}$, l. 143–160; full separability of measurement operators, l. 258; Result 2, l. 265–272;
  • the two-partite construction and the open question, Appendix C, l. 474–497.