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Using Graph Theory to Derive Inequalities for the Bell Numbers [article]

Alain Hertz and Anaelle Hertz and Hadrien Mélot
<span title="2021-10-19">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities  ...  for the Bell numbers.  ...  This close link between Bell numbers and graph colorings indicates that it is possible to use graph theory to derive inequalities for the Bell numbers. This is the aim of this article.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.00552v2">arXiv:2104.00552v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k3vizauhqzgmxmvyibghef472y">fatcat:k3vizauhqzgmxmvyibghef472y</a> </span>
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Bell monogamy relations in arbitrary qubit networks [article]

Minh Cong Tran, Ravishankar Ramanathan, Matthew McKague, Dagomir Kaszlikowski, Tomasz Paterek
<span title="2018-01-09">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation.  ...  We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits.  ...  This work is supported by the Singapore Ministry of Education Academic Research Fund  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1801.03071v1">arXiv:1801.03071v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gnapuz2oxzgztiumznors3k5a4">fatcat:gnapuz2oxzgztiumznors3k5a4</a> </span>
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Correlation Complementarity Yields Bell Monogamy Relations

P. Kurzyński, T. Paterek, R. Ramanathan, W. Laskowski, D. Kaszlikowski
<span title="2011-05-03">2011</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pkmpevvs3bgkhal5dvrmsu5mvq" style="color: black;">Physical Review Letters</a> </i> &nbsp;
We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum non-locality.  ...  In many cases, they yield tight quantum bounds on violation of single and multiple qubit correlation Bell inequalities.  ...  This bound is subsequently used to derive quantum bounds on Bell inequality violations. For its other applications see for instance Ref. [11] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.106.180402">doi:10.1103/physrevlett.106.180402</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/21635070">pmid:21635070</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bhb6sigtkfednjxsbey5cvkd4e">fatcat:bhb6sigtkfednjxsbey5cvkd4e</a> </span>
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Activation of monogamy in nonlocality using local contextuality

Debashis Saha, Ravishankar Ramanathan
<span title="2017-03-16">2017</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z3u6fzrh4fdvhnzujueyvzipwi" style="color: black;">Physical Review A</a> </i> &nbsp;
A unified view on the phenomenon of monogamy exhibited by Bell inequalities and non-contextuality inequalities arising from the no-signaling and no-disturbance principles is presented using the graph-theoretic  ...  We propose a novel type of trade-off, namely Bell inequalities that do not exhibit monogamy features of their own can be activated to be monogamous by the addition of a local contextuality term.  ...  We thank Remigiusz Augusiak and Marcin Pawłowski for helpful discussions. This work is supported by the NCN grant 2014/14/E/ST2/00020 and the ERC grant QOLAPS.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.95.030104">doi:10.1103/physreva.95.030104</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3kuspc4q5vfzviebnyqnz7gjwi">fatcat:3kuspc4q5vfzviebnyqnz7gjwi</a> </span>
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All two-party facet Bell inequalities are violated by Almost Quantum correlations [article]

Ravishankar Ramanathan
<span title="2020-04-16">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The methods also enable us to derive novel (almost) quantum Bell inequalities, which may be of independent interest for self-testing applications.  ...  We also exploit connections between the cut polytope of graph theory and the classical correlation Bell polytope, to show that correlation Bell inequalities that define facets of the lower dimensional  ...  We acknowledge useful discussions with Stefano Pironio, Paweł Horodecki and Andreas Winter. This  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.07673v1">arXiv:2004.07673v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cznjoppvenhajhioijml5cnhky">fatcat:cznjoppvenhajhioijml5cnhky</a> </span>
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Trade-offs in multiparty Bell-inequality violations in qubit networks

Ravishankar Ramanathan, Piotr Mironowicz
<span title="2018-08-27">2018</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z3u6fzrh4fdvhnzujueyvzipwi" style="color: black;">Physical Review A</a> </i> &nbsp;
Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.  ...  The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction.  ...  Now, in deriving monogamy relations using correlation complementarity, we encounter graphs with clique size ω(Γ) = 2|E(H)| = 2 n for an (n, 2, 2) inequality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.98.022133">doi:10.1103/physreva.98.022133</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kl3ixvm4qzb2ja4fq4zwqguqza">fatcat:kl3ixvm4qzb2ja4fq4zwqguqza</a> </span>
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From contextuality of a single photon to realism of an electromagnetic wave

Marcin Markiewicz, Dagomir Kaszlikowski, Paweł Kurzyński, Antoni Wójcik
<span title="2019-01-17">2019</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2jbq7znkzzdqzjy63ai2e6mpgq" style="color: black;">npj Quantum Information</a> </i> &nbsp;
We show that this fundamental difference between field intensities measurements and single photon detections shifts the classical bound of relevant Bell inequalities to its non-signaling limit, leaving  ...  Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell.  ...  ADDITIONAL INFORMATION Competing interests: The authors declare no competing interests.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/s41534-018-0117-8">doi:10.1038/s41534-018-0117-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3uig67s5znbg7agqlrqmcg3jbu">fatcat:3uig67s5znbg7agqlrqmcg3jbu</a> </span>
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From contextuality of a single photon to realism of an electromagnetic wave [article]

Marcin Markiewicz, Dagomir Kaszlikowski, Pawel Kurzynski, Antoni Wojcik
<span title="2018-01-08">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that this fundamental difference between field intensities measurements and single photon detections shifts the classical bound of relevant Bell inequalities to its algebraic limit, leaving no  ...  Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell.  ...  Non-applicability of the methods used to derive the quantum bound PQ with the E principle In [27] a general method of derivation of the maximal quantum bound for a given Bell-type scenario was introduced  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1801.02338v1">arXiv:1801.02338v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ovcphgxd6fclnjzj65hjy6234i">fatcat:ovcphgxd6fclnjzj65hjy6234i</a> </span>
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Bell Inequalities for Graph States

Otfried Gühne, Géza Tóth, Philipp Hyllus, Hans J. Briegel
<span title="2005-09-14">2005</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pkmpevvs3bgkhal5dvrmsu5mvq" style="color: black;">Physical Review Letters</a> </i> &nbsp;
To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states.  ...  We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits.  ...  Together with the exact calculation of DG for graphs with a small number of qubits this allows us to derive some general results for arbitrary graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.95.120405">doi:10.1103/physrevlett.95.120405</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/16197057">pmid:16197057</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lddvbtnirzaejarl5rgnmfg6qq">fatcat:lddvbtnirzaejarl5rgnmfg6qq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811223637/http://optics.szfki.kfki.hu/~toth/Publications/PRL05B.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/e6/bfe63973b97924fab3b9607618556f4880390762.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.95.120405"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Experimental Violation of Multipartite Bell Inequalities with Trapped Ions

B. P. Lanyon, M. Zwerger, P. Jurcevic, C. Hempel, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos
<span title="2014-03-13">2014</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pkmpevvs3bgkhal5dvrmsu5mvq" style="color: black;">Physical Review Letters</a> </i> &nbsp;
First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation  ...  Second we analyze GHZ states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially  ...  In this part we make use of general Bell-type inequalities derived for all graph states in Ref. [4] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.112.100403">doi:10.1103/physrevlett.112.100403</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24679272">pmid:24679272</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d2ud4hjkkvhx3oslmfhywxvymu">fatcat:d2ud4hjkkvhx3oslmfhywxvymu</a> </span>
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New Bell inequalities for the singlet state: Going beyond the Grothendieck bound

Itamar Pitowsky
<span title="">2008</span> <i title="AIP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nwwheyjjk5hnlmj6q5mtpqmmhi" style="color: black;">Journal of Mathematical Physics</a> </i> &nbsp;
However, if we go back to the original derivation by Bell, and use the perfect anti-correlation embodied in the singlet spin state, we can go beyond these bounds.  ...  Math. 163 499 (2006)) we prove that there are two-particle Bell inequalities for traceless two-outcome observables whose violation increases to infinity as the dimension and number of measurements grow  ...  In this paper we are using the fact that more inequalities are known for BELL(n) than for the general case BELL(n; m).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1063/1.2826227">doi:10.1063/1.2826227</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oactjsq2avf5bkhsmf3d7eynoe">fatcat:oactjsq2avf5bkhsmf3d7eynoe</a> </span>
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Error-Tolerating Bell Inequalities via Graph States [article]

Qing Chen, Sixia Yu, C.H. Oh
<span title="2009-03-19">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We investigate the Bell inequalities derived from the graph states with violations detectable even with the presence of noises, which generalizes the idea of error-correcting Bell inequalities [Phys.  ...  Secondly we construct also a single-error-tolerating Bell inequality with a violation that increases exponentially with the number of qubits.  ...  We acknowledge the financial support of NNSF of China (Grants No. 10705025, and No. 10675107) and the A*STAR Grant No. R-144-000-189-305.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0903.3318v1">arXiv:0903.3318v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vcpdxzeknffzbmfkzjcf3ridru">fatcat:vcpdxzeknffzbmfkzjcf3ridru</a> </span>
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Generalized Ardehali-Bell inequalities for graph states

Otfried Gühne, Adán Cabello
<span title="2008-03-21">2008</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
We derive Bell inequalities for graph states by generalizing the approach proposed by Ardehali [Phys. Rev. A 46, 5375 (1992)] for Greenberger-Horne-Zeilinger (GHZ) states.  ...  Using this method, we demonstrate that Bell inequalities with nonstabilizer observables are often superior to the optimal GHZ-Mermin-type (or stabilizer-type) Bell inequalities.  ...  Briegel for useful discussions and acknowledge support from the EU ͑OLAQUI, SCALA, and QICS͒, the FWF, the Junta de Andalucía Excellence Project No. P06-FQM-02243, and the Spanish MEC Project No.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.77.032108">doi:10.1103/physreva.77.032108</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ms5jfuketjhdfoyp3ljzl7xsb4">fatcat:ms5jfuketjhdfoyp3ljzl7xsb4</a> </span>
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On quantum sets of the multicoloured-graph approach to contextuality [article]

Lina Vandré, Marcelo Terra Cunha
<span title="2021-12-29">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The CHSH bipartite Bell scenario [...] is the most famous Bell scenario and leads to the best known and most used CHSH-Bell inequalities.  ...  graph is greater than or equal to the Lov\'asz number of the coloured graph.  ...  Acknowledgments We thank Fabian Bernards, Rafael Rabelo, and Elie Wolf for discussions. To formulate and solve the SDPs, we made use of the package NCPOL2SDPA [22] and MOSEK [23] solver.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.08561v3">arXiv:2105.08561v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cepi4dv2v5br3c7fj5qfzshyke">fatcat:cepi4dv2v5br3c7fj5qfzshyke</a> </span>
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Entropic Test of Quantum Contextuality

P. Kurzyński, R. Ramanathan, D. Kaszlikowski
<span title="2012-07-11">2012</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pkmpevvs3bgkhal5dvrmsu5mvq" style="color: black;">Physical Review Letters</a> </i> &nbsp;
Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves in [Phys. Rev.  ...  Lett. 61, 662 (1988)], that must be satisfied by all non-contextual theories. We find optimal measurements for violation of this inequality.  ...  We now focus on a three-level system and derive an entropic inequality analogous to the entropic Bell inequality in [8] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.109.020404">doi:10.1103/physrevlett.109.020404</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/23030134">pmid:23030134</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mz6p2pcq4zep5nobvimkdqnrti">fatcat:mz6p2pcq4zep5nobvimkdqnrti</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200828055833/https://arxiv.org/pdf/1201.2865v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/3d/f63dac5c7cb70f136515d255ff15cd56f6e8a63c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.109.020404"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>
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