Image reconstruction from photon sparse data

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the second spatial derivatives of the reconstructed image pixel intensities. The balance between these two terms is set by a bootstrapping technique where the target value of the log-likelihood term is deduced from a smoothed version of the original data. When compared to the original data, the processed images exhibit lower residuals with respect to the true object. We use photon-sparse data from two different experimental systems, one system based on a single-photon, avalanche photo-diode array and the other system on a time-gated, intensified camera. However, this same processing technique could most likely be applied to any low photon-number image irrespective of how the data is collected

The spatial state of non-interacting photons

High-dimensional quantum systems are becoming an increasingly important area of study. Due to their ability to encode more information than a two-dimensional system, high-dimensional systems are useful in many applications, from quantum communication to quantum computing. In particular, spatial states of light, such as orbital angular momentum and spatial position, are inherently high-dimensional by nature and lend themselves well to manipulation and measurement. As light is commonly used in communication applications, spatial states could extend the information capacity of quantum communication and make it easier to detect eavesdroppers in the system. This thesis comprises four experiments in which the spatial state of photons is manipulated and measured. The first experiment describes a filter for two dimensional anti-symmetric spatial states. We use a pair of photons entangled in multiple orbital angular momentum states in order to test the filter. We are able to manipulate which two-dimensional subspaces are in symmetric states and which are in anti-symmetric states, and as such we are able to filter out particular subspaces, effectively engineering high-dimensional states via Hong-Ou-Mandel interference. In the second experiment, we use the anti-symmetric state filter in a four-photon system. We begin with two pairs of photons, with entanglement within the pairs but not between the pairs. Combining one photon from each pair in our anti-symmetric state filter, we create entanglement between the other two photons, achieving entanglement swapping. Additionally, due to the two-dimensional nature of the filter, we transcribe entanglement into several two-dimensional subspaces in the process. In the third experiment, we investigate the quantum teleportation that occurs as a side effect of the entanglement swapping. We demonstrate teleportation of several two-dimensional OAM states, and we describe the result of attempted high dimensional teleportation. In the fourth and final experiment, we turn our attention from the OAM of light to the spatial position of light. Using our four-photon system and anti-symmetric state filter, we demonstrate ghost imaging between photons that have never interacted. This is enabled by taking advantage of the correlations produced when entanglement swapping occurs in the filter

Discriminating single-photon states unambiguously in high dimensions

The ability to uniquely identify a quantum state is integral to quantum science, but for non-orthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the non-deterministic protocol of unambiguous state discrimination (USD) enables error-free differentiation of states, at the cost of a lower frequency of success. We discriminate experimentally between non-orthogonal, high-dimensional states encoded in single photons; our results range from dimension $d=2$ to $d=14$. We quantify the performance of our method by comparing the total measured error rate to the theoretical rate predicted by minimum-error state discrimination. For the chosen states, we find a lower error rate by more than one standard deviation for dimensions up to $d=12$. This method will find immediate application in high-dimensional implementations of quantum information protocols, such as quantum cryptography.Comment: 4 pages + 3 pages supplementary, 4 figure

Quantum tests of causal structures and non-orthogonal states

This thesis details two experimental tests that can be applied to particular quantum states to reveal important information. We begin by discussing the relevant background in quantum information. We introduce qubits and qudits as basic quantum states, and we discuss the evolution and measurement of quantum states. We then discuss quantum state tomography as a means by which to obtain complete information about a state, followed by a discussion of state discrimination as a means by which to determine the state given the promise that it is drawn from some known set. We then discuss relevant experimental techniques in quantum optics, including measurement, generation of entanglement, and generation of single photons from entanglement. The first experiment we discuss deals with the causal structure of a system, which is the description of the origin of correlations between two or more states. The causal structure can be direct-cause, meaning that one state causes the other; common-cause, meaning that both states are caused by another; or hybrid-cause, which is a combination of the two. We perform the first implementation of a new type of tomography to determine the causal structure; this is called causal tomography and functions regardless of whether two qubits are related by a common state, a process, or some combination thereof. We implement a process on two entangled photons so that we can select the exact causal structure that results, which ranges continuously between direct-cause and common-cause structures. Using causal tomography, we recover causal structures that closely match expected results and demonstrate that quantum mechanics provides an advantage in causal inference. The second experiment we discuss deals with the unambiguous discrimination of multiple quantum states. For the first time, we apply the principles of unambiguous state discrimination to high-dimensional systems. Given a state chosen randomly out of d possible states encoded in d dimensions, we implement a procedure for determining which state was chosen; this procedure in theory functions without error. We encode and detect the states in the orbital angular momentum degree of freedom up to dimension d=14. Although no experiment can provide perfectly error-free measurement due to inevitable imperfections, we obtain an error rate below the theoretical error rate of minimum-error state discrimination for dimensions up to d=12. At the time of submission of this thesis, this work has been accepted for publication in Physical Review Letters

Simultaneous entanglement swapping of multiple orbital angular momentum states of light

Entanglement swapping generates remote quantum correlations between particles that have not interacted and is the cornerstone of long-distance quantum communication, quantum networks, and fundamental tests of quantum science. In the context of spatial modes of light, high-dimensional entanglement provides an avenue to increase the bandwidth of quantum communications and provides more stringent limits for tests of quantum foundations. Here we simultaneously swap the entanglement of multiple orbital angular momentum states of light. The system is based on a degenerate filter that cannot distinguish between different anti-symmetric states, and thus entanglement swapping occurs for several thousand pairs of spatial light modes simultaneously

Entangled Bessel beams

Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gauss (BG) basis. Having a readily adjustable radial scale, BG modes provide a more favourable basis for OAM entanglement over Laguerre-Gaussian (LG) modes. The OAM bandwidth in terms of BG modes can be increased by selection of particular radial modes and leads to a flattening of the spectrum. The flattening of the spectrum allows for higher entanglement. We demonstrate increased entanglement in terms of BG modes by performing a Bell-type experiment and violating the appropriate Clauser Horne Shimony Holt (CHSH) inequality. In addition, we reconstruct the quantum state of BG modes entangled in high-dimensions.Comment: 8 pages, 4 figure