#### Projects- Quantum computation and entanglement with ion strings
- Strongly interacting Fermi gases
- Dipolar quantum gases
- Quantum entanglement in higher-dimensional Hilbert spaces: foundations and applications
- Probing and controlling mesoscopic low-dimensional quantum systems
- Quantum agents, simulation and measurement-based computation
- Atom cavity QED
- Simulation of strongly correlated quantum systems
- Many-body quantum systems of cold atoms, molecules and ions
- A quantum switch for light
- Large-scale numerical simulations of quantum matter
- Entanglement in a CQED system
| # 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. | |