Higher dimensional time-energy entanglement

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.