Skip to main content
SpringerLink
Log in

Quantum Discord in Quantum Information Theory – From Strong Subadditivity to the Mother Protocol

  • Conference paper
  • First Online:
Theory of Quantum Computation, Communication, and Cryptography (TQC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6745))

Included in the following conference series:

  • 1855 Accesses

Abstract

Positivity of quantum discord is shown to be equivalent to the strong sub additivity of the von Neumann entropy. This leads to a connection between the mother protocol of quantum information theory [17] and quantum discord. We exploit this to show that discord is a measure coherence in the performance of the mother protocol. Since the mother protocol is a unification of an important class of problems (those that are bipartite, unidirectional and memoryless), we show discord to be a measure of coherence in these protocols. Our work generalizes an earlier operational interpretation of discord provided in terms of quantum state merging [10].

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Plenio, M.B., Virmani, S.: Quant. Inf. Comp. 7, 1 (2007)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Datta, A., Flammia, S.T., Caves, C.M.: Phys. Rev. A 72, 042316 (2005)

    Article  Google Scholar 

  4. Datta, A., Vidal, G.: Phys. Rev. A 75, 042310 (2007)

    Article  MathSciNet  Google Scholar 

  5. Zurek, W.H.: Ann. Phys. (Leipzig) 9, 855 (2000)

    Article  MathSciNet  Google Scholar 

  6. Ollivier, H., Zurek, W.H.: Phys. Rev. Lett. 88, 017901 (2002)

    Article  Google Scholar 

  7. Henderson, L., Vedral, V.: J. Phys. A: Math. Gen. 34, 6899 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Datta, A., Shaji, A., Caves, C.M.: Phys. Rev. Lett. 100, 050502 (2008)

    Article  Google Scholar 

  9. Eastin, B.: arxiv:1006.4402 (2010)

    Google Scholar 

  10. Madhok, V., Datta, A.: Phys. Rev. A 83, 032323 (2011)

    Article  Google Scholar 

  11. Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Phys. Rev. A 83, 032324 (2011)

    Article  Google Scholar 

  12. Datta, A.: Studies on the role of entanglement in mixed-state quantum computation, Ph.D thesis, University of New Mexico, arxiv:0807.4490 (2008)

    Google Scholar 

  13. Lieb, E.H., Ruskai, M.B.: J. Math. Phys. 12, 1938 (1973)

    Google Scholar 

  14. Cover, T., Thomas, J.: Elements of Information Theory. Wiley & Sons, New York (2006)

    MATH  Google Scholar 

  15. Horodecki, M., Oppenheim, J., Winter, A.: Nature 436, 673 (2005)

    Article  Google Scholar 

  16. Horodecki, M., Oppenheim, J., Winter, A.: Comm. Math. Phys. 268, 107 (2007)

    MathSciNet  Google Scholar 

  17. Abeyesinghe, A., Devetak, I., Hayden, P., Winter, A.: Proc. R. Soc. A 465, 2537 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Devetak, I., Harrow, A.W., Winter, A.: IEEE Trans. Inf. Theory 54, 4587 (2008)

    Article  MathSciNet  Google Scholar 

  19. Horodecki, M., Horodecki, P., Horodecki, R., Leung, D.W., Terhal, B.M.: Quantum Inf. Comput. 1, 70 (2001)

    MATH  MathSciNet  Google Scholar 

  20. Devetak, I., Winter, A.: Proc. R. Soc. Lond. A 461, 207 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Devetak, I., Winter, A.: Phys. Rev. Lett. 93, 080501 (2004)

    Article  MathSciNet  Google Scholar 

  22. Schumacher, B.: Phys. Rev. A 54, 2614 (1996)

    Article  Google Scholar 

  23. Schumacher, B., Nielsen, M.A.: Phys. Rev. A 54, 2629 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the EPSRC (EP/H03031X/1), the EC integrated project Q-ESSENCE, US European Office of Aerospace Research (FA8655-09-1-3020), and the Center for Quantum Information and Control (CQuIC) where this work was done, and NSF Grant Nos. 0903953 and 0903692.

Author information

Authors and Affiliations

  1. Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM, 87131-0001, USA

    Vaibhav Madhok

  2. Clarendon Laboratory, Department of Physics, University of Oxford, OX1 3PU, Oxford, UK

    Animesh Datta

Authors
  1. Vaibhav Madhok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Animesh Datta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Animesh Datta .

Editor information

Editors and Affiliations

  1. University of Washington, Seattle, Washington, USA

    Dave Bacon

  2. Universidad Complutense de Madrid, Madrid, Spain

    Miguel Martin-Delgado

  3. NEC Laboratories America, Princeton, New Jersey, USA

    Martin Roetteler

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Madhok, V., Datta, A. (2014). Quantum Discord in Quantum Information Theory – From Strong Subadditivity to the Mother Protocol. In: Bacon, D., Martin-Delgado, M., Roetteler, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2011. Lecture Notes in Computer Science(), vol 6745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54429-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54429-3_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54428-6

  • Online ISBN: 978-3-642-54429-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation