Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

How quantum is a quantum ensemble?

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In the Hilbert space operator formalism of quantum mechanics, a single quantum state, which is represented by a density operator, can be regarded as classical in the sense that it can always be diagonalized. However, a quantum ensemble, which is represented by a family of quantum states together with a probability distribution specifying the probability of the occurrence of each state, cannot be diagonalized simultaneously in generic cases, and possesses intrinsic quantum features as long as the involved quantum states are not commutative. The natural question arises as how to quantify its quantumness. By virtue of a canonical correspondence between quantum ensembles and classical-quantum bipartite states, we propose an intuitive entropic quantity which captures certain quantum features of quantum ensembles, and compare it with that defined as the gap between the Holevo quantity and the accessible information. Implications for quantum cryptography and relations to quantum channel capacities are indicated. Some illustrative examples are worked out.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Alicki R., Van Ryn N.: A simple test of quantumness for a single system. J. Phys. A 41, 062001 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  2. Alicki R., Piani M., Van Ryn N.: Quantumness witnesses. J. Phys. A 41, 495303 (2008)

    Article  MathSciNet  Google Scholar 

  3. Holevo A.S.: Bounds for the quantity of information transmitted by a quantum communication channel. Problems Inform. Trans. 9, 177 (1973)

    MathSciNet  Google Scholar 

  4. Davis E.B.: Information and quantum measurement. IEEE Trans. Inform. Theory IT 24, 596 (1978)

    Article  Google Scholar 

  5. Peres A., Wootters W.K.: Optimal detection of quantum information. Phys. Rev. Lett. 66, 1119 (1991)

    Article  ADS  PubMed  Google Scholar 

  6. Jozsa R., Robb D., Wootters W.K.: Lower bound for accessible information in quantum mechanics. Phys. Rev. A 49, 668 (1994)

    Article  CAS  MathSciNet  ADS  PubMed  Google Scholar 

  7. Hausladen P., Wootters W.K.: A “pretty-good” measurement for distinguishing quantum states. J. Mod. Opt. 41, 2385 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Fuchs, C.A.: Distinguishability and accessible information in quantum theory, arXiv:quant-ph/9601020 (1996)

  9. Sasaki M., Barnett S.M., Jozsa R., Osaki M., Hirota O.: Accessible information and optimal strategies for real symmetrical quantum sources. Phys. Rev. A 59, 3325 (1999)

    Article  CAS  ADS  Google Scholar 

  10. Fuchs, C.A.: Just two nonorthogonal quantum states, arXiv:quant-ph/9810032 (1998)

  11. Fuchs, C.A., Sasaki, M.: The quantumness of a set of quantum states, arXiv:quant-ph/0302108 (2003)

  12. Ollivier H., Zurek W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2002)

    Article  ADS  PubMed  Google Scholar 

  13. Henderson L., Vedral V.: Classical, quantum and total correlation. J. Phys. A 34, 6899 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Vedral V., Plenio M.B., Rippin M.A., Knight P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  MATH  CAS  MathSciNet  ADS  Google Scholar 

  15. Henderson L., Vedral V.: Information, relative entropy of entanglement, and irreversibility. Phys. Rev. Lett. 84, 2263 (2000)

    Article  CAS  ADS  PubMed  Google Scholar 

  16. Vedral V.: The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74, 197 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  17. Rajagopal A.K., Rendell R.W.: Separability and correlations in composite states based on entropy methods. Phys. Rev. A 66, 022104 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  18. Usha Devi A.R., Rajagopal A.K.: Generalized information theoretic measure to discern the quantumness of correlations. Phys. Rev. Lett. 100, 140502 (2008)

    Article  CAS  PubMed  Google Scholar 

  19. Werner R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

    Article  ADS  PubMed  Google Scholar 

  20. Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  21. Horodecki M.: Entanglement measures. Quantum Inform. Comp. 1, 3 (2001)

    MATH  MathSciNet  Google Scholar 

  22. Piani M., Horodecki P., Horodecki R.: No-local-broadcasting theorem for multipartite quantum correlations. Phys. Rev. Lett. 100, 090502 (2008)

    Article  ADS  PubMed  Google Scholar 

  23. Luo S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  24. Li N., Luo S.: Classical states versus separable states. Phys. Rev. A 78, 024303 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  25. Ohya M., Petz D.: Quantum Entropy and Its Use. Springer, Berlin (1993)

    MATH  Google Scholar 

  26. Partovi M.H.: Correlative capacity of composite quantum states. Phys. Rev. Lett. 103, 230502 (2009)

    Article  ADS  PubMed  Google Scholar 

  27. Luo S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  28. Horodecki, M., Horodecki, P., Horodecki, R., Piani, M.: Quantumness of ensemble from no-broadcasting principle, arXiv:quant-ph/0506174 (2005)

  29. Luo S., Li N., Cao X.: Relative entropy between quantum ensembles. Periodica Math.Hung. 59, 223 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Shunlong Luo & Nan Li

  2. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, H3G 1M8, Canada

    Wei Sun

Authors
  1. Shunlong Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shunlong Luo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luo, S., Li, N. & Sun, W. How quantum is a quantum ensemble?. Quantum Inf Process 9, 711–726 (2010). https://doi.org/10.1007/s11128-010-0162-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-010-0162-5

Keywords

Search

Navigation