Towards teleporting quantum images

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Achieving higher dimensionality in quantum protocols is receiving increasing interest at the promise of a range of benefits, starting from increased information capacity to noise resilience. This also arises naturally in many quantum systems, from the multitude of photonic states in the temporal, frequency or spatial domains to many atomic levels in an atom. Generalising these to superpositions of states with unique amplitude and phases, we can call such encoded information quantum images. The ability to transfer, either the state of a system directly or information encoded as quantum images thus becomes a pressing frontier with teleportation an important building block. Bearing two distinct features, teleportation forms a fundamentally different way of communicating such that the information does not pass directly between communicating parties and when used with quantum carriers, can form the basis for a variety of quantum networks, starting from quantum repeaters to a type of quantum computing. In this thesis, the over-arching goal involves physically implementing a highdimensional system in an effort towards teleporting quantum images. To do so, Chapter 1 considers the basic language, protocol, characterising techniques and spatial states being used in this work. We then consider bringing in nonlinear optical strategies to the physical implementation of both the generation and detection aspects in Chapter 2. Particular emphasis is made on orbital angular momentum (OAM) states as they are used as a test-bed for our spatial degree of freedom. For this property, the naturally generated states in spontaneous parametric down-conversion are considered where the amplitude structure is neglected and an in-depth investigation done. Here, we look at the radial modal purities in both the generational and detection aspects of such phaseonly structuring and emphasise the general nature with experiments spanning from quantum to classical. Mitigating measures and corrective steps are also introduced which show the effects of maintaining the naturally-preserved eigenmode structures of the wave-equation. Next, the time-reversed phenomenon, sum-frequency generation, was explored as a detection mechanism. We test this classically by interacting different modal structures and looking at the generated modes. In doing so, we showed that the phase-flattening nature of conjugate states in the interaction allows for modal detection that is not confined to the same wavelength. The measurement-conditioned process could then be modelled in quantum formalism as reverse SPDC and introduced as a projector for quantum teleportation. Chapter 3 explores the full theoretical formalism of a non-linear detection-based teleportation system for spatial modes, which is numerically modelled for OAM and implemented as a test-bed. Here, the physical system was characterised and control explored by changing the generation and detection mode sizes. In doing so, we demonstrated a 15-dimensional teleportation system in OAM that exceeds the viii classical limit and extended the implementation to include a variety of states across different bases, extending from polar to Cartesian coordinates. We achieved this by encoding the information on bright coherent laser light. Despite this protocol extending to quantum carriers, present inefficiencies in the non-linear interaction require many copies to to be present, stimulating the process and yielding what we call stimulated teleportation. While the ability to develop efficiencies is both beyond the scope of this work and an active area of research, with promising advances in metasurfaces, we look towards how this system may be further applied and enhanced in Chapter 4. Notably, we numerically map out an optimisation space for pixel states and look at requirements for teleporting images of complex objects, directly. Here, we derive a technique for characterising such teleportation, based on single pixel quantum ghost imaging where signal at higher resolution is conserved, wavelength dependency is lessened and the ability to fully distinguish the complex spatial structure; the latter being is an active challenge in quantum imaging systems. Further applications are also discussed where pump engineering could lead to better fidelities, how a deterministic system could be implemented and how hybrid entanglement channels could lead to the teleportation of hybrid entangled states.
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, School of Physics, University of the Witwatersrand, Johannesburg, 2023
Quantum, Orbital angular momentum (OAM)