Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities

Journal name:
Nature Physics
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Published online

Quantum entanglement1, 2 plays a vital role in many quantum-information and communication tasks3. Entangled states of higher-dimensional systems are of great interest owing to the extended possibilities they provide. For example, they enable the realization of new types of quantum information scheme that can offer higher-information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems (see ref. 4 and references therein). Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher-dimensional entangled systems are used5. We have measured previously untested correlations between two photons to experimentally demonstrate high-dimensional entangled states. We obtain violations of Bell-type inequalities generalized to d-dimensional systems6 up to d=12. Furthermore, the violations are strong enough to indicate genuine 11-dimensional entanglement. Our experiments use photons entangled in orbital angular momentum7, generated through spontaneous parametric down-conversion8, 9, and manipulated using computer-controlled holograms.

At a glance


  1. Schematic representation of experimental set-up for violations of Bell-type inequalities.
    Figure 1: Schematic representation of experimental set-up for violations of Bell-type inequalities.

    C(Aa=v,Bb=w) or C(θAa,θBb) is the coincidence count rate when SLM A is in state |vright fenceaA or |θAaright fence and SLM B is in state |wright fencebB or |θBbright fence respectively.

  2. Coincidence count rate (self-normalized) as a function of the relative orientation angle between state analysers ([theta]A-[theta]B).
    Figure 2: Coincidence count rate (self-normalized) as a function of the relative orientation angle between state analysers (θAθB).

    Equation (5) for a state with maximal 11-dimensional entanglement is fitted to the experimental data with the vertical offset and amplitude left as free parameters. Errors were estimated assuming Poisson statistics.

  3. Experimental Bell-type parameter Sd versus number of dimensions d.
    Figure 3: Experimental Bell-type parameter Sd versus number of dimensions d.

    Sd>2 violates local realism for any d≥2. The plot compares the theoretically predicted violations by a maximally entangled state and the LHV limit with the experiments. Violations are observed for up to d=12. Errors were estimated assuming Poisson statistics.

  4. Experimental coincidence rates proportional to the probability of measuring the state  with [ell]s,[ell]i=-5,[hellip],+5.
    Figure 4: Experimental coincidence rates proportional to the probability of measuring the state with s,i=−5,…,+5.

    The coloured and greyed-out bars depict the measurement results with and without the application of Procrustean filtering respectively. The measurement time was 20s for each combination of s and i.


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  1. SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

    • Adetunmise C. Dada,
    • Gerald S. Buller &
    • Erika Andersson
  2. Department of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, UK

    • Jonathan Leach &
    • Miles J. Padgett


A.C.D. and E.A. devised the concept of the experiment. E.A. supervised the theoretical aspects of the project. G.S.B. and M.J.P. advised on aspects of experimental design. A.C.D. and J.L. carried out the experiment. A.C.D. and E.A. wrote the paper with contributions from all authors.

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