Multipartite entanglement in quantum optical systems

In this project we investigate properties of novel, highly entangled states of light. For this purpose we combine theoretical with experimental effort to progress towards a new understanding of quantum phenomena in multi-particle systems.

The approaches we will pursue are motivated by the multipartite entangled states accessible in experiments: matrix product states (MPS) and Gaussian states. Important states for quantum information processing like W, GHZ and cluster states are described very efficiently as MPS. In practice, imperfect versions of these states will be produced. We will develop a description for the relevant decoherence processes and study the entanglement properties of the resulting noisy MPS states. Gaussian states have been thoroughly studied in quantum information. We will enhance the knowledge about their entanglement properties by relating them to general multipartite states. One such relation is given by the central limit theorem. The entanglement properties of the initial state are preserved in many cases¹⁾ and can then be studied in the Gaussian setting. We will analyse which entanglement properties survive and generalise this consideration to other limiting procedures. Conversely, many non-Gaussian states can be obtained from the former by simple operations; e. g. photon-subtracted states are obtained conditionally on certain photo-detection events. Drawing on qualitative and quantitative results on Gaussian states we will determine the properties of their “descendants”. Since Gaussian entangled states are a readily available resource, we will study how to use them optimally to produce non-Gaussian states and derive practical criteria to verify the entanglement properties of the latter.

Such states can be generated experimentally using spontaneous parametric down-conversion (SPDC)^{2, 3)}, but, so far, all experiments have essentially been limited to 4 photons. We propose to advance research by developing, in close collaboration with Dr. Apolonskiy (LMU, project A.1.1), a dedicated mode-locked laser system capable of generating bright short pulses (360 nJ, 100 fs, 11 MHz). This will enable in a standard SPDC set-up first the observation and analysis of a variety of polarisation entangled 6-photon states. After refining the method with periodically poled crystals or hollow fibres a significantly larger number will be achieved. Compared with other methods in QIP, SPDC has the advantage that a significant amount of entanglement is already provided by the source, significantly reducing the number of quantum operations.

The other approach is to employ the coherence between different pulses to define entangled qudit pairs. High-dimensional interferometers will be designed for manipulation and analysis of novel quantum states. In this experiment the transition from qubit to qudit all the way to continuous systems can be directly followed on a single quantum system. We will use fibre networks and stable high-Q cavities to cover the whole range of interest. Ultimately, we will combine the approaches to study high-dimensional, entangled multi-photon states.