Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantifying entanglement in macroscopic systems

Abstract

Traditionally, entanglement was considered to be a quirk of microscopic objects that defied a common-sense explanation. Now, however, entanglement is recognized to be ubiquitous and robust. With the realization that entanglement can occur in macroscopic systems — and with the development of experiments aimed at exploiting this fact — new tools are required to define and quantify entanglement beyond the original microscopic framework.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: A way of generating entangled photons by using down conversion.
Figure 2: Separable states.
Figure 3: Susceptibility as a macroscopic witness of entanglement.

References

  1. 1

    Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Many-body entanglement. Rev. Mod. Phys. 80, 517–576 (2008).

    CAS  ADS  Article  Google Scholar 

  2. 2

    Osterloh, A. et al. Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002).

    CAS  ADS  Article  Google Scholar 

  3. 3

    Osborne, T. J. & Nielsen, M. A. Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Arnesen, M. C., Bose, S. & Vedral, V. Natural thermal and magnetic entanglement in 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001).

    CAS  ADS  Article  Google Scholar 

  5. 5

    Vedral, V. High temperature macroscopic entanglement. New J. Phys. 6, 102 (2004).

    ADS  Article  Google Scholar 

  6. 6

    Brukner, C., Vedral, V. & Zeilinger, A. Crucial role of entanglement in bulk properties of solids. Phys. Rev. A 73, 012110 (2006).

    ADS  Article  Google Scholar 

  7. 7

    Vedral, V. A better than perfect match. Nature 439, 397 (2006).

    CAS  ADS  Article  Google Scholar 

  8. 8

    Zeilinger, A., Weihs, G., Jennewein, T. & Aspelmeyer, M. Happy centenary, photon. Nature 433, 230–238 (2005).

    CAS  ADS  Article  Google Scholar 

  9. 9

    Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935).

    CAS  ADS  Article  Google Scholar 

  10. 10

    Werner, R. F. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989).

    CAS  ADS  Article  Google Scholar 

  11. 11

    Brukner, C. & Vedral, V. Macroscopic thermodynamical witnesses of quantum entanglement. Preprint at <http://arxiv.org/abs/quant-ph/0406040> (2004).

  12. 12

    Toth, G. & Guhne, O. Detecting genuine multipartite entanglement with two local measurements. Phys. Rev. Lett. 94, 060501 (2004).

    Article  Google Scholar 

  13. 13

    Narnhoffer, H. Separability for lattice systems at high temperature. Phys. Rev. A 71, 052326 (2005).

    ADS  Article  Google Scholar 

  14. 14

    Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812; 823–828; 844–849 (1935).

    ADS  Article  Google Scholar 

  15. 15

    Horodecki, M., Horodecki, P. & Horodecki, R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996).

    CAS  ADS  MathSciNet  Article  Google Scholar 

  16. 16

    Anders J. & Vedral, V. Macroscopic entanglement and phase transitions. Open Sys. Inform. Dyn. 14, 1–16 (2007).

    MathSciNet  Article  Google Scholar 

  17. 17

    Horodecki, M. Entanglement measures. Quant. Inform. Comput. 1, 3–26 (2001).

    MathSciNet  MATH  Google Scholar 

  18. 18

    Vedral V. et al. Quantifying entanglement. Phys. Rev. Lett. 78, 2275–2279 (1997).

    CAS  ADS  MathSciNet  Article  Google Scholar 

  19. 19

    Greenberger, D., Horne, M. A. & Zeilinger, A. in Bell's Theorem, Quantum Theory, and Conceptions of the Universe (ed. Kafatos, M.) 73–76 (Kluwer Academic, Dordrecht, 1989).

    Google Scholar 

  20. 20

    Dur, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000).

    ADS  MathSciNet  Article  Google Scholar 

  21. 21

    Leggett, A. J. Macroscopic quantum systems and the quantum theory of measurement. Prog. Theor. Phys. Suppl. 69, 80–100 (1980).

    ADS  MathSciNet  Article  Google Scholar 

  22. 22

    Anders, J. & Winter, A. Entanglement and separability of quantum harmonic oscillator systems at finite temperature. Quant. Inform. Comput. 8, 0245–0262 (2008).

    MathSciNet  MATH  Google Scholar 

  23. 23

    Vedral, V. Entanglement in the second quantisation formalism. Cent. Eur. J. Phys. 2, 289–306 (2003).

    Google Scholar 

  24. 24

    Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 81, 53–60 (1973).

    Google Scholar 

  25. 25

    Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).

    CAS  ADS  Article  Google Scholar 

  26. 26

    Chandran, A., Kaszlikowski, D., Sen De, A., Sen, U. & Vedral, V. Regional versus global entanglement in resonating-valence-bond states. Phys. Rev. Lett. 99, 170502 (2007).

    ADS  Article  Google Scholar 

  27. 27

    Page, D. N. & Wootters, W. K. Evolution without evolution: dynamics described by stationary observables. Phys. Rev. D 27, 2885–2892 (1983).

    ADS  Article  Google Scholar 

  28. 28

    Haffner, H. et al. Scalable multiparticle entanglement of trapped ions. Nature 438, 643–646 (2005).

    CAS  ADS  Article  Google Scholar 

  29. 29

    Lu, C.-Y. et al. Experimental entanglement of six photons in graph states. Nature Phys. 3, 91–95 (2007).

    CAS  ADS  Article  Google Scholar 

  30. 30

    Baugh, J. et al. Quantum information processing using nuclear and electron magnetic resonance: review and prospects. Preprint at <http://arxiv.org/abs/0710.1447> (2007).

  31. 31

    de Chiara, G. et al. A scheme for entanglement extraction from a solid. New J. Phys. 8, 95 (2006).

    Article  Google Scholar 

  32. 32

    Toth, G. Entanglement detection in optical lattices of bosonic atoms with collective measurements. Phys. Rev. A 69, 052327 (2004).

    ADS  Article  Google Scholar 

  33. 33

    Heaney, L., Anders, J., Kaszlikowski, D. & Vedral, V. Spatial entanglement from off-diagonal long-range order in a Bose–Einstein condensate. Phys. Rev. A 76, 053605 (2007).

    ADS  Article  Google Scholar 

  34. 34

    Recher, P. & Loss, D. Superconductor coupled to two Luttinger liquids as an entangler for spin electrons. Phys. Rev. B 65, 165327 (2002).

    ADS  Article  Google Scholar 

  35. 35

    Verstraete, F. & Cirac, J. I. Quantum nonlocality in the presence of superselection rules and data hiding protocols. Phys. Rev. Lett. 91, 010404 (2003).

    CAS  ADS  MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

I am grateful for funding from the Engineering and Physical Sciences Research Council, the Wolfson Foundation, the Royal Society and the European Union. My work is also supported by the National Research Foundation (Singapore) and the Ministry of Education (Singapore). I thank J. A. Dunningham, A. J. Leggett, D. Markham, E. Rieper, W. Son and M. Williamson for discussions of this and related subjects. W. Son's help with illustrations is also gratefully acknowledged.

Author information

Affiliations

Authors

Ethics declarations

Competing interests

The author declares no competing financial interests.

Additional information

Correspondence should be addressed to the author (vlatko.vedral@quantuminfo.org).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vedral, V. Quantifying entanglement in macroscopic systems. Nature 453, 1004–1007 (2008). https://doi.org/10.1038/nature07124

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing