Quantum Entanglement in High-Dimensional Systems
Large entangled quantum systems are required for many quantum information applications such as quantum computation or quantum communication. Additionally, they are also a fruitful playground for fundamental questions, such as violations of local realism or classification of entanglement classes. The size of an entangled quantum system depends on both the number of involved parties and the dimensions.
We investigate high-dimensional entanglement of photons encoded in transverse spatial modes – in particular modes carrying discrete quanta of orbital angular momentum (OAM). In contrast to the well-known property of polarization (which has two settings, thus can carry one bit of information), much more information can be encoded in the OAM of photons. We have shown that two photons can be entangled in more than 100 dimensions . Furthermore, quantum entanglement with up to 10.000ħ of angular momentum has been achieved in our labs, showing that systems with very large quanta can still possess the puzzling properties of the quantum world .
Furthermore, we created for the first time an entangled quantum state where both the number of particles and the number of dimension are larger than two . In such systems, surprising new structures of asymmetric entanglement occur . For example, a hierarchy can emerge where particle A is four-dimensionally entangled with party B and C, while B and C are only two-dimensionally entangled with the rest. In addition, only very recently new types of violations of local realism have been found which can be applied to multi-particle high-dimensional quantum states . Besides fundamental questions, they might lead to new ways for quantum communication or quantum error correction.
The generation of complex high-dimensional quantum states is difficult in the laboratory. Not only because of stringent alignment requirements, but also because the involved phenomena are quite counter-intuitive. Thus in many situations it is not even clear how to find quantum experiments. For that we have developed a computer algorithm, which can propose new experimentally feasible setups .
Several of these computer-designed experiments have already been successful implemented in the laboratories [3,7]. Recently we showed that automated designs of quantum optical experiments by algorithms can not only produce specific quantum states or transformations, but can also be a source for inspiration for new techniques – which can further be investigated by human scientists in a broader context.
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 Fickler, R., Campbell, G. T., Buchler, B. C., Lam, P. K., & Zeilinger, A. Quantum entanglement of angular momentum states with quantum numbers up to 10010. arXiv:1607.00922 PNAS (in press), (2016).
 Malik, M., Erhard, M., Huber, M., Krenn, M., Fickler, R., & Zeilinger, A. Multi-photon entanglement in high dimensions. Nature Photonics, 10(4), 248-252 (2016).
 Huber, M., & de Vicente, J. I. Structure of multidimensional entanglement in multipartite systems. Physical review letters, 110(3), 030501 (2013).
 Lawrence, J. Rotational covariance and Greenberger-Horne-Zeilinger theorems for three or more particles of any dimension. Physical Review A, 89(1), 012105 (2014).
 Krenn, M., Malik, M., Fickler, R., Lapkiewicz, R., & Zeilinger, A. Automated search for new quantum experiments. Physical review letters, 116(9), 090405. (2016).
 Schlederer, F., Krenn, M., Fickler, R., Malik, M., & Zeilinger, A. Cyclic transformation of orbital angular momentum modes. New Journal of Physics, 18(4), 043019 (2016).
 Krenn, M., Hochrainer, A., Lahiri, M., & Zeilinger, A. Entanglement by Path Identity. arXiv:1610.00642 (2016).