Skip to main content
SpringerLink
Log in

Measuring quantumness: from theory to observability in interferometric setups

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We investigate the notion of quantumness based on the noncommutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. We show that such a quantity can be experimentally measured with an interferometric setup and that, when an arbitrary bipartition of a given composite system is introduced, it detects the one-way quantum correlations restricted to one of the two subsystems. We finally show that, by combining only two projective measurements and carrying out the interference procedure, our measure becomes an efficient universal witness of quantum discord and nonclassical correlations.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  Google Scholar 

  2. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    Article  ADS  Google Scholar 

  3. K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  4. R. Alicki, N. Van Ryn, J. Phys. A 41, 062001 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  5. R. Alicki, M. Piani, N. Van Ryn, J. Phys. A 41, 495303 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  6. P. Facchi, S. Pascazio, V. Vedral, K. Yuasa, J. Phys. A 45, 105302 2012

    Article  ADS  MathSciNet  Google Scholar 

  7. P. Facchi, L. Ferro, G. Marmo, S. Pascazio, J. Phys. A 47, 035301 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  8. R. Fazio, K. Modi, S. Pascazio, V. Vedral, K. Yuasa, Phys. Rev. A 87, 052132 (2013)

    Article  ADS  Google Scholar 

  9. J. Grabowski, M. Kuś, G. Marmo, J. Phys. A 44, 175302 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  10. F. Benatti, R. Floreanini, U. Marzolino, Ann. Phys. 327, 1304 (2012)

    Article  ADS  Google Scholar 

  11. A.P. Balachandran, T.R. Govindarajan, A.R. de Queiroz, A.F. Reyes-Lega, Phys. Rev. Lett. 110, 080503 (2013)

    Article  ADS  Google Scholar 

  12. P. Pfeiffer, I.L. Egusquiza, M. Di Ventra, M. Sanz, E. Solano, Sci. Rep. 6, 29507 (2016)

    Article  ADS  Google Scholar 

  13. M. Sanz, L. Lamata, E. Solano, APL Photon. 3, 080801 (2018)

    Article  ADS  Google Scholar 

  14. M.-L. Hu, H. Fan, Phys. Rev. A 95, 052106 (2017)

    Article  ADS  Google Scholar 

  15. S. Bhattacharya, S. Banerjee, A.K. Pati, Q. Inf. Proc. 17, 236 (2018)

    Article  Google Scholar 

  16. J. Jing, L.-A. Wu, A. del Campo, Sci. Rep. 6, 38149 (2016)

    Article  ADS  Google Scholar 

  17. N. Mirkin, F. Toscano, D.A. Wisniacki, Phys. Rev. A 94, 052125 (2016)

    Article  ADS  Google Scholar 

  18. X. Liu, W. Wu, C. Wang, Phys. Rev. A 95, 052118 (2017)

    Article  ADS  Google Scholar 

  19. N. Lambert, Y.-N. Chen, Y.-C. Cheng, C.-M. Li, G.-Y. Chen, F. Nori, Nat. Phys. 9, 10 (2013)

    Article  Google Scholar 

  20. P. Iyengar, G.N. Chandan, R. Srikanth, https://doi.org/arXiv:1312.1329 (2013)

  21. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932) [English translation: Mathematical Foundations of Quantum Mechanics, (Princeton University Press, Berlin, 1955)]

  22. H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  23. L. Henderson, V. Vedral, J. Phys. A 34, 6899 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  24. E. Sjöqvist, A.K. Pati, A. Ekert, J.S. Anandan, M. Ericsson, D.K.L. Oi, V. Vedral, Phys. Rev. Lett. 85, 2845 (2000)

    Article  ADS  Google Scholar 

  25. R. Filip, Phys. Rev. A 65, 062320 (2002)

    Article  ADS  Google Scholar 

  26. H.A. Carteret, Phys. Rev. Lett. 94, 040502 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  27. A.K. Ekert, C.M. Alves, D.K.L. Oi, M. Horodecki, P. Horodecki, L.C. Kwek, Phys. Rev. Lett. 88, 217901 (2002)

    Article  ADS  Google Scholar 

  28. C.K. Hong, Z.Y. Ou, L. Mandel, Phys. Rev. Lett. 59, 2044 1987

    Article  ADS  Google Scholar 

  29. J.-S. Jin, F.-Y. Zhang, C.-S. Yu, H.-S. Song, J. Phys. A 45, 115308 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  30. D. Girolami, G. Adesso, Phys. Rev. Lett. 108, 150403 (2012)

    Article  ADS  Google Scholar 

  31. M. Gessner, M. Ramm, T. Pruttivarasin, A. Buchleitner, H.-P. Breuer, H. Häffner, Nat. Phys. 10, 105 (2014)

    Article  Google Scholar 

  32. G. Passante, O. Moussa, D.A. Trottier, R. Laflamme, Phys. Rev. A 84, 044302 (2011)

    Article  ADS  Google Scholar 

  33. R. Blandino, M.G. Genoni, J. Etesse, M. Barbieri, M.G.A. Paris, P. Grangier, R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012)

    Article  ADS  Google Scholar 

  34. C. Benedetti, A.P. Shurupov, M.G.A. Paris, G. Brida, M. Genovese, Phys. Rev. A 87, 052136 (2013)

    Article  ADS  Google Scholar 

  35. L. Chen, E. Chitambar, K. Modi, G. Vacanti, Phys. Rev. A 83, 020101 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INFN, Sezione di Napoli, Napoli, 80126, Italy

    Leonardo Ferro, Fabrizio Illuminati & Giuseppe Marmo

  2. Morgan Stanley Analytics, 1095, Budapest, Hungary

    Leonardo Ferro

  3. Abdus Salam ICTP, Strada Costiera 11, 34151, Trieste, Italy

    Rosario Fazio

  4. NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, 56126, Pisa, Italy

    Rosario Fazio

  5. Dipartimento di Ingegneria Industriale, Università di Salerno, Fisciano (SA), 84084, Italy

    Fabrizio Illuminati

  6. Dipartimento di Fisica, Università di Napoli, Napoli, 80126, Italy

    Giuseppe Marmo

  7. Dipartimento di Fisica and MECENAS, Università di Bari, Bari, 70126, Italy

    Saverio Pascazio

  8. Istituto Nazionale di Ottica (INO-CNR), 50125, Firenze, Italy

    Saverio Pascazio

  9. INFN, Sezione di Bari, 70126, Bari, Italy

    Saverio Pascazio

  10. Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK

    Vlatko Vedral

  11. Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore, Singapore

    Vlatko Vedral

  12. Department of Physics, National University of Singapore, 2 Science Drive 3, 117542, Singapore, Singapore

    Vlatko Vedral

Authors
  1. Leonardo Ferro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rosario Fazio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fabrizio Illuminati
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Giuseppe Marmo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Saverio Pascazio
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Vlatko Vedral
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saverio Pascazio.

Additional information

Contribution to the Topical Issue “Quantum Correlations”, edited by Marco Genovese, Vahid Karimipour, Sergei Kulik, and Olivier Pfister.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferro, L., Fazio, R., Illuminati, F. et al. Measuring quantumness: from theory to observability in interferometric setups. Eur. Phys. J. D 72, 219 (2018). https://doi.org/10.1140/epjd/e2018-90522-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2018-90522-y

Search

Navigation