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
- Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935). , &
- Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23 807–812; 823–828; 844–849 (1935).
- 2000). & Quantum Computation and Quantum Information (Cambridge Univ. Press,
- Security of quantum key distributions with entangled qudits. Phys. Rev. A 69, 032313 (2004). , , &
- Closing the detection loophole in Bell experiments using qudits. Phys. Rev. Lett. 104, 060401 (2010). , &
- Bell inequalities for arbitrarily high dimensional systems. Phys. Rev. Lett. 88, 040404 (2002). , , , &
- Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992). , , &
- New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995). et al.
- Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion. Phys. Rev. A 69, 023811 (2004). , , &
- Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993). et al.
- Schemes for teleportation of an unknown single-qubit quantum state by using an arbitrary high-dimensional entangled state. Chinese Phys. Lett. 27, 10307–10310 (2010). , , &
- Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992). &
- Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991).
- Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999). , &
- Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312 (2003). , &
- Experimental demonstration of a BDCZ quantum repeater node. Nature 454, 1098–1101 (2008). et al.
- Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state. Nature Phys. 6, 331–335 (2010). et al.
- Experimental two-photon, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89, 240401 (2002). , &
- Experimental realization of Einstein–Podolsky–Rosen–Bohm gedankenexperiment: A new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982). , &
- Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces. Opt. Exp. 17, 8287–8293 (2009). et al.
- Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces. Phys. Rev. A 81, 043844 (2010). et al.
- Precise quantum tomography of photon pairs with entangled orbital angular momentum. New J. Phys. 11, 103024 (2009). et al.
- Shannon dimensionality of quantum channels and its application to photon entanglement. Phys. Rev. Lett. 101, 120502 (2008). et al.
- Experimental quantum cryptography with qutrits. New J. Phys. 8, 75 (2006). , , , &
- Violations of local realism with quantum systems described by N-dimensional Hilbert spaces up to N=16. Phys. Rev. A 64, 024101 (2001). , &
- Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996). , , &
- Vortex knots in light. New J. Phys. 7, 55 (2005). , , &
- Quantum spiral bandwidth of entangled two-photon states. Phys. Rev. A 68, 050301 (2003). , &
- Analysis and interpretation of high transverse entanglement in optical parametric down conversion. Phys. Rev. Lett. 92, 127903 (2004). &
- Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum. Phys. Rev. Lett. 91, 227902 (2003). , , , &
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