IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v414y2014icp204-215.html
   My bibliography  Save this article

Tsallis entropy for assessing quantum correlation with Bell-type inequalities in EPR experiment

Author

Listed:
  • Chapeau-Blondeau, François

Abstract

A new Bell-type inequality is derived through the use of the Tsallis entropy to quantify the dependence between the classical outcomes of measurements performed on a bipartite quantum system, as typical of an EPR experiment. This new inequality is confronted with standard correlation-based Bell inequalities, and with other known Bell-type inequalities based on the Shannon entropy for which it constitutes a generalization. For an optimal range of the Tsallis order, the new inequality is able to detect nonlocal quantum correlation with measurements from a larger set of quantum observables. In this respect it is more powerful and also complementary compared to the previously known Bell-type inequalities.

Suggested Citation

  • Chapeau-Blondeau, François, 2014. "Tsallis entropy for assessing quantum correlation with Bell-type inequalities in EPR experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 204-215.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:204-215
    DOI: 10.1016/j.physa.2014.07.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114006372
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.07.053?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Abe, Sumiyoshi & Rajagopal, A.K, 2001. "Nonadditive conditional entropy and its significance for local realism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 157-164.
    2. Canosa, N. & Rossignoli, R. & Portesi, M., 2006. "Majorization properties of generalized thermal distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 435-441.
    3. Abe, Sumiyoshi, 2002. "Nonadditive entropies and quantum entanglement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 306(C), pages 316-322.
    4. Majtey, A.P. & Plastino, A.R. & Plastino, A., 2012. "New features of quantum discord uncovered by q-entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2491-2499.
    5. James M Chappell & Azhar Iqbal & Derek Abbott, 2012. "N-Player Quantum Games in an EPR Setting," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    6. Canosa, N. & Rossignoli, R., 2003. "Generalized entropies and quantum entanglement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(3), pages 371-376.
    7. Abe, Sumiyoshi, 2004. "Quantum q-divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 359-365.
    8. Nicolas Brunner & Noah Linden, 2013. "Connection between Bell nonlocality and Bayesian game theory," Nature Communications, Nature, vol. 4(1), pages 1-6, October.
    9. Rossignoli, R. & Canosa, N., 2004. "Generalized disorder measures and the detection of quantum entanglement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 637-643.
    10. Canosa, N. & Rossignoli, R., 2005. "General non-additive entropic forms and the inference of quantum density operators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 121-130.
    11. Stanislaw Drozdz & Jaroslaw Kwapien & Pawel Oswiecimka & Rafal Rak, 2010. "The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect," Papers 1011.2385, arXiv.org.
    12. Canosa, N. & Rossignoli, R. & Portesi, M., 2006. "Majorization relations and disorder in generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 126-129.
    13. Tsallis, Constantino & Lamberti, Pedro W. & Prato, Domingo, 2001. "A nonextensive critical phenomenon scenario for quantum entanglement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 158-171.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gillard, Nicolas & Belin, Etienne & Chapeau-Blondeau, François, 2018. "Enhancing qubit information with quantum thermal noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 219-230.
    2. Miśkiewicz, Janusz, 2016. "Improving quality of sample entropy estimation for continuous distribution probability functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 473-485.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gillard, Nicolas & Belin, Etienne & Chapeau-Blondeau, François, 2018. "Enhancing qubit information with quantum thermal noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 219-230.
    2. Izadkhah, Salman & Amini-Seresht, Ebrahim & Moradian, Ali, 2023. "Sufficient conditions for the majorization ordering and their applications in some quantum information comparisons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    3. Bosyk, G.M. & Sergioli, G. & Freytes, H. & Holik, F. & Bellomo, G., 2017. "Approximate transformations of bipartite pure-state entanglement from the majorization lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 403-411.
    4. Iqbal, Azhar & Chappell, James M. & Abbott, Derek, 2015. "Social optimality in quantum Bayesian games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 798-805.
    5. Alves, L.G.A. & Ribeiro, H.V. & Santos, M.A.F. & Mendes, R.S. & Lenzi, E.K., 2015. "Solutions for a q-generalized Schrödinger equation of entangled interacting particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 35-44.
    6. Yildiz, Anil & Mern, John & Kochenderfer, Mykel J. & Howland, Michael F., 2023. "Towards sequential sensor placements on a wind farm to maximize lifetime energy and profit," Renewable Energy, Elsevier, vol. 216(C).
    7. Provash Mali & Amitabha Mukhopadhyay, 2015. "Multifractal characterization of gold market: a multifractal detrended fluctuation analysis," Papers 1506.08847, arXiv.org.
    8. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.
    9. Nayak, Anantha S. & Sudha, & Rajagopal, A.K. & Usha Devi, A.R., 2016. "Bipartite separability of symmetric N-qubit noisy states using conditional quantum relative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 286-295.
    10. Wang, Jian & Huang, Menghao & Zhang, Yudong & Kim, Junseok, 2022. "Modification of multifractal analysis based on multiplicative cascade image," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    11. Stanis{l}aw Dro.zd.z & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek & Marcin Wk{a}torek, 2019. "Signatures of crypto-currency market decoupling from the Forex," Papers 1906.07834, arXiv.org, revised Jul 2019.
    12. Stanisław Drożdż & Ludovico Minati & Paweł Oświȩcimka & Marek Stanuszek & Marcin Wa̧torek, 2019. "Signatures of the Crypto-Currency Market Decoupling from the Forex," Future Internet, MDPI, vol. 11(7), pages 1-18, July.
    13. Ishak, Nur Izzati & Muniandy, S.V. & Chong, Wu Yi, 2021. "Entropy analysis of the discrete-time quantum walk under bit-flip noise channel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    14. Shi, Lian & Xu, Feng & Chen, Yongtai, 2021. "Quantum Cournot duopoly game with isoelastic demand function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    15. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Pawe{l} O'swic{e}cimka & Marek Stanuszek, 2018. "Multifractal cross-correlations between the World Oil and other Financial Markets in 2012-2017," Papers 1812.08548, arXiv.org, revised Jun 2019.
    16. Basnarkov, Lasko & Stojkoski, Viktor & Utkovski, Zoran & Kocarev, Ljupco, 2019. "Correlation patterns in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1026-1037.
    17. Mali, Provash & Mukhopadhyay, Amitabha, 2014. "Multifractal characterization of gold market: A multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 361-372.
    18. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    19. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    20. Łukasz Bil & Dariusz Grech & Magdalena Zienowicz, 2017. "Asymmetry of price returns—Analysis and perspectives from a non-extensive statistical physics point of view," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-24, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:204-215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.