Separation of quantum, spatial quantum, and approximate quantum correlations

Salman Beigi

doi:10.22331/q-2021-01-28-389

Separation of quantum, spatial quantum, and approximate quantum correlations

QuOne Lab, Phanous Research and Innovation Centre, Tehran, Iran

Published:	2021-01-28, volume 5, page 389
Eprint:	arXiv:2004.11103v2
Doi:	https://doi.org/10.22331/q-2021-01-28-389
Citation:	Quantum 5, 389 (2021).

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Abstract

Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model, various notions of sets of quantum correlations can be defined. In this paper we prove separations of such sets of quantum correlations. In particular, we show that the set of bipartite quantum correlations with four binary measurements per party becomes strictly smaller once we restrict the local Hilbert spaces to be finite dimensional, $\textit{i.e.}$, $\mathcal{C}_{\text{$\rm{q}$}}^{(4, 4, 2,2)} \neq \mathcal{C}_{\text{$\rm{qs}$}}^{(4, 4, 2,2)}$. We also prove non-closure of the set of bipartite quantum correlations with four ternary measurements per party, $\textit{i.e.}$, $\mathcal{C}_{\text{$\rm{qs}$}}^{(4, 4, 3,3)} \neq \mathcal{C}_{\text{$\rm{qa}$}}^{(4, 4, 3,3)}$.

► BibTeX data

@article{Beigi2021separationof,
  doi = {10.22331/q-2021-01-28-389},
  url = {https://doi.org/10.22331/q-2021-01-28-389},
  title = {Separation of quantum, spatial quantum, and approximate quantum correlations},
  author = {Beigi, Salman},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {389},
  month = jan,
  year = {2021}
}

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Cited by

[1] Shubhayan Sarkar and Remigiusz Augusiak, "Self-testing of multipartite Greenberger-Horne-Zeilinger states of arbitrary local dimension with arbitrary number of measurements per party", Physical Review A 105 3, 032416 (2022).

[2] Connor Paddock, William Slofstra, Yuming Zhao, and Yangchen Zhou, "An Operator-Algebraic Formulation of Self-testing", Annales Henri Poincaré (2023).

[3] Shubhayan Sarkar, "Certification of entangled quantum states and quantum measurements in Hilbert spaces of arbitrary dimension", arXiv:2302.01325, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-12-06 19:44:44) and SAO/NASA ADS (last updated successfully 2023-12-06 19:44:45). The list may be incomplete as not all publishers provide suitable and complete citation data.

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