High-dimensional entanglement in the spatial basis

Abstract

Modern cryptography today is required to protect sensitive and important data from attackers. With the dawn of quantum computing, these classical cryptography methods are under threat, which implies that cryptography methods have to be adapted. Quantum cryptography is a promising solution to this problem, that makes use of the concept of quantum entanglement to encrypt information in various degrees of freedom of quantum systems, such as photons. The basics of quantum entanglement, applied to photons, is explored with the aim of extending it to quantum cryptography. The fundamentals of structured light are investigated, discussed and applied in conjunction with the field of quantum entanglement. Quantum entanglement as a concept is used with the spatial basis of light, namely the theoretically infinite orbital angular momentum basis, to understand the change in entanglement prop erties as the transition is made from two-dimensional entanglement, using qubits, to higher-dimensional entanglement up to a dimension of four. The optical setup, along with some of the most important equipment and optics are discussed and explored to explain how theory translates to experiment. With the well-known concept of coincidence counting, numerous quantum experiments such as the spiral spectrum, quantum state tomography and Bell violation tests were performed. Finally, quantum key distribution as an application of spatial quantum entanglement is used to illustrate its capabilities and to make the understanding of the fundamentals of quantum entanglement application ready. The overall observation made is that as the dimension of the quantum system under consideration was increased, by increasing the amount of elements in the chosen basis, the overall accuracy of measurements decreased. This included the spiral bandwidth, the Bell parameter used in Bell violation tests, the fidelity in quantum state tomography state reconstruction and the quantum bit error rate calculated for the well-known BB84 and E91 quantum key distribution algorithms. Another observation made was that precise alignment was really important, as quantum systems are extremely sensitive. Any loss of light effected results greatly. The noise usually associated with quantum systems was also observed, especially where quantum state tomography and quantum key distribution was concerned. This was measured through a decreased overall state fidelity