Experimental EPR-steering using Bell-local states

Journal name:
Nature Physics
Volume:
6,
Pages:
845–849
Year published:
DOI:
doi:10.1038/nphys1766
Received
Accepted
Published online
Corrected online

The concept of ‘steering’ was introduced in 1935 by Schrödinger1 as a generalization of the EPR (Einstein–Podolsky–Rosen) paradox. It has recently been formalized as a quantum-information task with arbitrary bipartite states and measurements2, for which the existence of entanglement is necessary but not sufficient. Previous experiments in this area3, 4, 5, 6 have been restricted to an approach7 that followed the original EPR argument in considering only two different measurement settings per side. Here we demonstrate experimentally that EPR-steering occurs for mixed entangled states that are Bell local (that is, that cannot possibly demonstrate Bell non-locality). Unlike the case of Bell inequalities8, 9, 10, 11, increasing the number of measurement settings beyond two—we use up to six—significantly increases the robustness of the EPR-steering phenomenon to noise.

At a glance

Figures

  1. The steering task.
    Figure 1: The steering task.

    Bob is sceptical that Alice can remotely affect (steer) his state. Bob trusts his measuring device (represented by the white box), in particular that it behaves according to the laws of quantum mechanics, but makes no assumptions about Alice’s system and devices (represented by the black box). The steps in the task, from top (1) to bottom (4) are as follows. (1) Bob receives his qubit. He is unsure whether he has received (a) half of an entangled pair or (b) a pure state sent by Alice. (2) After Bob receives his qubit, he announces to Alice his choice of measurement setting from the set . (3) Bob records his own measurement results σkB and receives the result Ak that Alice declares. (4) Bob combines the results to calculate (over many runs) the steering parameter Sn. If this is greater than a certain bound, Alice has demonstrated steering of Bob’s state, and thus Bob can be sure that he received a, not b.

  2. Platonic-solid measurement schemes.
    Figure 2: Platonic-solid measurement schemes.

    Measurement axes uk are defined by the Bloch-space directions through antipodal pairs of vertices of regular figures. ae, Square, n=2 (a), and the four suitable Platonic solids: octahedron, n=3 (b); cube, n=4 (c); icosahedron, n=6 (d), and dodecahedron, n=10 (e). The bullet symbols show the orientations of pure states in optimal cheating ensembles for two-qubit Werner states. In d and e these states align with the measurement axes (vertices), but in ac they have the dual arrangement, on the face centres, similar to the situation in random-access codes28.

  3. Experimental set-up.
    Figure 3: Experimental set-up.

    Pairs of identical photons are produced using type-I SPDC and directed, by single-mode fibres, to a linear-optics controlled-Z logic gate. After the gate, qubit 1 passes through a pair of Hanle wedge DPs. By varying the azimuthal angle between the optical axes of the DPs, we control the amount of depolarizing noise, which sets μ (see Methods). Abbreviations: SMFC, single-mode fibre coupler; MMFC, multi-mode fibre coupler.

  4. Experimental demonstration of S3 steering with Bell-local states.
    Figure 4: Experimental demonstration of S3 steering with Bell-local states.

    Data for tests of Bell non-locality (using the two-setting Bell–CHSH inequality) and EPR-steering using our three-setting inequality. The horizontal dashed line is the Bell–CHSH inequality bound, and the vertical dashed line is the S3 bound. The diagonal blue line shows the predicted values for Werner states of varying μ. Each data point corresponds to a different experimentally produced Werner state. Error bars represent one standard deviation, and are calculated from Poissonian counting statistics.

  5. EPR-steering and /`cheating/' strategies for increasing n.
    Figure 5: EPR-steering and ‘cheating’ strategies for increasing n.

    The four plots show the measured EPR-steering correlation Sn for various Werner states against their tomographically reconstructed values of μ, for n=2,3,4 and 6. The blue diagonal line in each plot represents the theoretical value of Sn. The vertical shaded regions represent different entanglement classes for Werner states. Left to right: separable; non-separable but not steerable (even for ); steerable but not Bell non-local; potentially Bell non-local; Bell non-local by the simple Bell–CHSH test. (For 0.7071>μ>0.7056, there is a positive Bell-non-locality test using 465 settings a side11.) The red solid horizontal line represents the Sn theoretically attainable by a ‘cheating’ strategy by Alice. This is the face-centred ensemble, except for n=6, where it is the vertex ensemble. This defines the steering bound Cn—EPR-steering is demonstrated if Sn exceeds this. As in Fig. 1, the orange solid line (slightly below Cn) represents the experimentally attained value using the optimal cheating ensemble. The square highlights a state that is both steerable for n=2 and n=3 and also Bell non-local. The circle and right-pointing triangle show states that become steerable as n increases, from n=2 to n=3 and n=4 to n=6 respectively. The diamond is a state that is steerable for two different measurement schemes and is Bell local. The up-pointing triangle is not steerable, whereas the down-pointing triangle is steerable in principle but could not be steered using any of the finite-n inequalities implemented by us. Error bars (shown only when large enough to be clearly seen) are one standard deviation and are calculated from Poissonian counting statistics.

Change history

Corrected online 02 November 2011
The authors wish to point out that there were systematic errors in some of the demonstrations of Alice's optimal attempt to cheat (orange lines in Fig. 5, for n = 3, 4 and 6), due to misalignment of the waveplates. The data have been retaken with the corrected settings and are included in Fig. 5 (the plot for n = 2 is unchanged). The arguments of the paper are unaffected by this correction. These changes have been made in the PDF and HTML versions of this Letter.

References

  1. Schrödinger, E. Discussion of probability relations between separated systems. Proc. Camb. Phil. Soc. 31, 555563 (1935).
  2. Wiseman, H. M., Jones, S. J. & Doherty, A. C. Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007).
  3. Ou, Z. Y., Pereira, S. F., Kimble, H. J. & Peng, K. C. Realization of the Einstein–Podolsky–Rosen paradox for continuous variables. Phys. Rev. Lett. 68, 36633666 (1992).
  4. Bowen, W. P., Schnabel, R., Lam, P. K. & Ralph, T. C. Experimental investigation of criteria for continuous variable entanglement. Phys. Rev. Lett. 90, 043601 (2003).
  5. Hald, J., Sørensen, J. L., Schori, C. & Polzik, E. S. Spin squeezed atoms: A macroscopic entangled ensemble created by light. Phys. Rev. Lett. 83, 13191322 (1999).
  6. Howell, J. C., Bennink, R. S., Bentley, S. J. & Boyd, R. W. Realization of the Einstein–Podolsky–Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92, 210403 (2004).
  7. Reid, M. D. Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification. Phys. Rev. A 40, 913923 (1989).
  8. Altepeter, J. B. et al. Experimental methods for detecting entanglement. Phys. Rev. Lett. 95, 033601 (2005).
  9. Acìn, A., Gisin, N. & Toner, B. Grothendieck’s constant and local models for noisy entangled quantum states. Phys. Rev. A 73, 062105 (2006).
  10. Brunner, N. & Gisin, N. Partial list of bipartite Bell inequalities with four binary settings. Phys. Lett. A 372, 31623167 (2008).
  11. Vértesi, T. More efficient Bell inequalities for Werner states. Phys. Rev. A 78, 032112 (2008).
  12. Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777780 (1935).
  13. Reid, M. D. et al. Colloquium: The Einstein–Podolsky–Rosen paradox: From concepts to applications. Rev. Mod. Phys. 81, 17271751 (2009).
  14. Cavalcanti, E. G., Jones, S. J., Wiseman, H. M. & Reid, M. D. Experimental criteria for steering and the EPR paradox. Phys. Rev. A. 80, 032112 (2009).
  15. Jones, S. J., Wiseman, H. M. & Doherty, A. C. Entanglement, Einstein–Podolsky–Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A 76, 052116 (2007).
  16. White, A. G. et al. Measuring two-qubit gates. J. Opt. Soc. Am. B 24, 172183 (2007).
  17. Barrett, J. Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality. Phys. Rev. A 65, 042302 (2002).
  18. Werner, R. F. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 42774281 (1989).
  19. Bell, J. S. On the Einstein–Podolsky–Rosen paradox. Physics (Long Island City, N.Y.) 1, 195200 (1964).
  20. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880884 (1969).
  21. Kwiat, P. G., Waks, E., White, A. G., Appelbaum, I. & Eberhard, P. H. Ultrabright source of polarization-entangled photons. Phys. Rev. A 60, R773R776 (1999).
  22. O’Brien, J. L. et al. Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264267 (2003).
  23. Langford, N. K. et al. Demonstration of a simple entangling optical gate and its use in Bell-state analysis. Phys. Rev. Lett. 95, 210504 (2005).
  24. Kiesel, N. et al. Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505 (2005).
  25. Okamoto, R., Hofmann, H. F., Takeuchi, S. & Sasaki, K. Demonstration of an optical quantum controlled-not gate without path interference. Phys. Rev. Lett. 95, 210506 (2005).
  26. Puentes, G., Voigt, D., Aiello, A. & Woerdman, J. P. Tunable spatial decoherers for polarization-entangled photons. Opt. Lett. 31, 20572059 (2006).
  27. James, D. F. V., Kwiat, P. G., Munro, W. J. & White, A. G. Measurement of qubits. Phys. Rev. A 64, 052312 (2001).
  28. Spekkens, R. W. et al. Preparation contextuality powers parity-oblivious multiplexing. Phys. Rev. Lett. 102, 010401 (2009).

Download references

Author information

Affiliations

  1. Centre for Quantum Dynamics, Griffith University, Brisbane 4111, Australia

    • D. J. Saunders,
    • S. J. Jones,
    • H. M. Wiseman &
    • G. J. Pryde
  2. Centre for Quantum Computer Technology, Australian Research Council, Australia

    • D. J. Saunders,
    • S. J. Jones,
    • H. M. Wiseman &
    • G. J. Pryde

Contributions

H.M.W. conceived the theory. S.J.J. and H.M.W. developed the theory. G.J.P. developed the experiment. H.M.W. and G.J.P. supervised the project. D.J.S. built the experiment, and collected and analysed the data. D.J.S., S.J.J., H.M.W. and G.J.P. composed the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to:

Author details

Additional data