Foundations and Applications of Quantum Science

Quantum entanglement in higher-dimensional Hilbert spaces: foundations and applications

Anton Zeilinger
Sven Ramelow

Quantum entanglement in higher-dimensional Hilbert spaces promises novel fundamental phenomena and opens up new applications for processing and communicating quantum information. We propose to realize such higher-dimensional states, both of single photons and of entangled photons. There are two methods of choice: firstly, we will study various infinite-dimensional systems of photon states featuring non-conventional wave fronts and states where the vectorial character of the solutions of the Maxwell equations comes into play, implying a nontrivial difference from matter waves. Secondly, we propose to create single and entangled photon states in multimodal waveguides, which constitutes a novel direction in coherent integrated optics. In principle, this allows any unitary operator in a higher-dimensional Hilbert space to be realized in a compact and precise manner. It enables the observation of novel Einstein-Podolsky-Rosen correlations and opens up the investigation of new fundamental questions such as the connection between unbiased bases. One of the most intriguing and important open questions is how many mutually unbiased bases exist in a Hilbert space with a dimension not given by the power of a prime. Mutually unbiased bases are also very important as entanglement witnesses, and we will investigate the general connection between the two in Hilbert spaces of arbitrary dimension.

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Created by: Rainer Blatt
Last modified 2013-01-31T12:03:00 by Tracy Northup