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Experimental determination of entanglement with a single measurement

Nature volume 440, pages 1022–1024 (2006)Cite this article

Abstract

Nearly all protocols requiring shared quantum information1—such as quantum teleportation2 or key distribution3—rely on entanglement between distant parties. However, entanglement is difficult to characterize experimentally. All existing techniques for doing so, including entanglement witnesses4,11,12 or Bell inequalities5, disclose the entanglement of some quantum states but fail for other states; therefore, they cannot provide satisfactory results in general. Such methods are fundamentally different from entanglement measures that, by definition, quantify the amount of entanglement in any state. However, these measures suffer from the severe disadvantage that they typically are not directly accessible in laboratory experiments. Here we report a linear optics experiment in which we directly observe a pure-state entanglement measure, namely concurrence6. Our measurement set-up includes two copies of a quantum state: these ‘twin’ states are prepared in the polarization and momentum degrees of freedom of two photons, and concurrence is measured with a single, local measurement on just one of the photons.

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Figure 1: Experimental set-up for the measurement of entanglement using two copies of the quantum state.
Figure 2: Count rates.
Figure 3: Experimental values of concurrence.

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References

  1. Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, UK, 2000)

    MATH  Google Scholar 

  2. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  3. Ekert, A. K. Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  5. Bell, J. S. On the Einstein Podolsky Rosen paradox. Physics 1, 195–200 (1964)

    Article  MathSciNet  Google Scholar 

  6. Bennet, C. H., DiVincenzo, D. P., Smolin, J. A. & Wootters, W. K. Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  7. Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev Lett. 80, 2245–2248 (1998)

    Article  ADS  CAS  Google Scholar 

  8. Vidal, G. & Werner, R. F. Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  9. Sancho, J. M. G. & Huelga, S. F. Measuring the entanglement of bipartite pure states. Phys. Rev. A 61, 042303 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  10. White, A., James, D., Eberhard, P. & Kwiat, P. Nonmaximally entangled states: Production, characterization, and utilization. Phys. Rev. Lett. 83, 3103–3107 (1990)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Leibfried, D. et al. Creation of a six-atom ‘Schrödinger cat’ state. Nature 438, 639–642 (2005)

    Article  ADS  CAS  Google Scholar 

  13. Horodecki, P. Measuring quantum entanglement without prior state reconstruction. Phys. Rev. Lett. 90, 167901 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  14. Mintert, F., Kuś, M. & Buchleitner, A. Concurrence of mixed multi-partite quantum states. Phys. Rev. Lett. 95, 260502 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  15. Brun, T. A. Measuring polynomial functions of states. Quant. Inform. Comput. 4, 401–408 (2004)

    MathSciNet  MATH  Google Scholar 

  16. Kwiat, P. G. Hyper entangled states. J. Mod. Opt. 44, 2173–2184 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  17. Barbieri, M., Cinelli, C., Mataloni, P. & Martini, F. D. Polarization-momentum hyperentangled states: Realization and characterization. Phys. Rev. A 72, 052110 (2005)

    Article  ADS  Google Scholar 

  18. Boschi, D., Branca, S., DeMartini, F., Hardy, L. & Popescu, S. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121–1125 (1998)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  19. Englert, B.-G., Kurtsiefer, C. & Weinfurter, H. Universal unitary gate for single-photon two-qubit states. Phys. Rev. A 63, 032303 (2003)

    Article  ADS  Google Scholar 

  20. Kwiat, P. G., Waks, E., White, A. G., Appelbaum, I. & Eberhard, P. H. Ultrabright source of polarization-entangled photons. Phys. Rev. A 60, R773–R776 (1999)

    Article  ADS  CAS  Google Scholar 

  21. Rarity, J. & Tapster, P. Experimental violation of Bell's inequality based on phase and momentum. Phys. Rev. Lett. 64, 2495–2498 (1990)

    Article  ADS  CAS  Google Scholar 

  22. Fiorentino, M. & Wong, F. N. C. Deterministic controlled-not gate for single-photon two-qubit quantum logic. Phys. Rev. Lett. 93, 070502 (2004)

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge support from the Brazilian agencies CNPq, CAPES, PRONEX, FUJB and FAPERJ. This work was performed as part of the Brazilian Millennium Institute for Quantum Information, and was supported by a fellowship within the postdoctoral programme of the German Academic Exchange Service (DAAD) as well as by a Feodor Lynen fellowship of the Alexander von Humboldt foundation. We are indebted to C. H. Monken for discussions.

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Authors and Affiliations

  1. Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972, Rio de Janeiro, Brazil

    S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich & F. Mintert

  2. Department of Physics, Harvard University, Massachusetts, 02138, Cambridge, USA

    F. Mintert

  3. Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187, Dresden, Germany

    A. Buchleitner

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  1. S. P. Walborn
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  5. A. Buchleitner
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Correspondence to S. P. Walborn.

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Walborn, S., Souto Ribeiro, P., Davidovich, L. et al. Experimental determination of entanglement with a single measurement. Nature 440, 1022–1024 (2006). https://doi.org/10.1038/nature04627

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