Higher dimensional time-energy entanglement
Daniel Richart · 2014
Judging by the compelling number of innovations based on taming quantum mechanical effects, such as the development of transistors and lasers, further research in this field promises to tackle further technological challenges in the years to come. This statement gains even more importance in the information processing scenario. Here, the growing data generation and the correspondingly higher need for more efficient computational resources and secure high bandwidth networks are central problems which need to be tackled. In this sense, the required CPU minituarization makes the design of structures at atomic levels inevitable, as foreseen by Moore's law. From these perspectives, it is necessary to concentrate further research efforts into controlling and manipulating quantum mechanical systems. This enables for example to encode quantum superposition states to tackle problems which are computationally NP hard and which therefore cannot be solved efficiently by classical computers. The only limitation affecting these solutions is the low scalability of existing quantum systems. Similarly, quantum communication schemes are devised to certify the secure transmission of quantum information, but are still limited by a low transmission bandwidth. This thesis follows the guideline defined by these research projects and aims to further increase the scalability of the quantum mechanical systems required to perform these tasks. The method used here is to encode quantum states into photons generated by spontaneous parametric down-conversion (SPDC). An intrinsic limitation of photons is that the scalability of quantum information schemes employing them is limited by the low detection efficiency of commercial single photon detectors. This is addressed by encoding higher dimensional quantum states into two photons, increasing the scalability of the scheme in comparison to multi-photon states. Further on, the encoding of quantum information into the emission-time degree of freedom improves its applicability to long distance quantum communication schemes. By doing that, the intrinsic limitations of other schemes based on the encoding into the momentum and polarization degree of freedom are overcome. This work presents results on a scalable experimental implementation of time-energy encoded higher dimensional states, demonstrating the feasibility of the scheme. Further tools are defined and used to characterize the properties of the prepared quantum states, such as their entanglement, their dimension and their preparation fidelity. Finally, the method of quantum state tomography is used to fully determine the underlying quantum states at the cost of an increased measurement effort and thus operation time. It is at this point that results obtained from the research field of compressed sensing help to decrease the necessary number of measurements. This scheme is compared with an adaptive tomography scheme designed to offer an additional reconstruction speedup. These results display the scalability of the scheme to bipartite dimensions higher than 2x8, equivalent to the encoding of quantum information into more than 6 qubits.