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. \n \nThe 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. \n \nThe 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.
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. \n \nThe 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. \n \nThe 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.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated
Entanglement is the resource that most sharply distinguishes quantum information processing from its classical counterpart, and this thesis examines it from two complementary directions: how it can be detected and quantified, and how it, together with the broader machinery of quantum correlations, interference, and measurement, can be put to use. We first study two simple, measurable conditions that detect bipartite entanglement, and show that the extent to which either is violated yields a lower bound on the negativity of a state. The bound is established for two qubits, extended to systems of arbitrary finite dimension, and sharpened when partial knowledge of the Schmidt vectors is available. We then turn to discrete-outcome quantum sensor networks, in which one seeks only to determine which detectors, or which group or spatial pattern of detectors, has responded to a signal. Working in the weak-interaction regime, where the output states are nonorthogonal, we use minimum-error and unambiguous state discrimination to show that entangled initial states and collective measurements confer an advantage when detectors are grouped, and we develop a shift-operator formalism that gives closed-form success probabilities for the detection of shifted patterns in one- and two-dimensional arrays. Next we consider the problem of learning two unknown pure qubit states, together with their probabilities of occurrence, from a scrambled stream; we show that receiving the systems in identically prepared pairs supplies exactly the extra quantum information needed, since the resulting two-qubit state in the symmetric subspace has a unique decomposition into pure product states, which we recover by tomography. Finally, we show how interference and measurement can convert information encoded in the phases of quantum amplitudes into information encoded in their magnitudes, amplifying the amplitudes that carry useful information and suppressing those that do not, and we apply this technique to states produced by the quantum approximate optimization algorithm for the MaxCut and minimum-vertex-cover problems. Throughout, a single theme recurs: the correlations and superpositions permitted by quantum mechanics are at once something to be measured and something to be exploited.
To date, quantum theory is the most successful physical theory that has been discovered. However, there is still the possibility that an inconsistency between experimental observations and the predictions of quantum theory may one day be found, thus prompting the replacement of quantum theory with a superior, post-quantum theory. To narrow down the scope of possibilities for the true theory that describes nature, one can perform experiments that falsify other physical theories, by demonstrating an incompatibility between experimental observations and the predictions of these theories. This thesis details two such experiments. First we provide relevant background information, beginning with a review of experimental quantum optics. Next, we review noncontextual ontological theories and discuss requirements for experimental tests of such theories. Finally, we discuss the framework of generalised probabilistic theories before introducing the two experiments. \n \n \nThe first experiment is a test of noncontextual ontological (or hidden-variable) models of nature. An ontological model of a physical theory is one in which systems have preexisting properties, and a noncontextual ontological model is one in which systems that are indistinguishable experimentally are represented identically in the model. Physical theories that cannot be represented by a noncontextual ontological model are said to be nonclassical; quantum theory is an example of such a physical theory that is nonclassical in this sense. Prior to this thesis, experimental tests of the assumption of noncontextuality had assumed that the experiments were free of both systematic and statistical errors, which is not justifiable for any experiment. We introduce new analytical techniques that allow us to avoid making these assumptions, and perform an experiment with single photons that, with high confidence, rules out the possibility of describing nature with a noncontextual ontological model. \n \n \nThe second experiment is a demonstration of self-consistent state and measurement tomography in the framework of generalised probabilistic theories (GPTs). The GPT framework is a very general, operationally-motivated framework for describing a physical theory in terms of the observable events predicted by the theory. We develop a technique for inferring the GPT description of a set of states and measurements directly from experimental data. By analysing our data in this general framework, we are able to test various candidate physical theories of nature. We perform an experiment with single photons, and quantify the size of possible variations between quantum theory and the true physical theory that describes nature.
The nascent field of quantum information offers the promise of dramatic speed increases for certain types of computation and logical protocols which are classically impossible. The phenomenon of nonlocality is fundamental to this study, and polarization-entangled photons o er a clean, bright, and stable system for its experimental investigation. This thesis investigates, both experimentally and theoretically, the creation, manipulation, and measurement of polarization-entangled photon pairs. Our entangled photon pairs are created through spontaneous parametric down-conversion within a pair of adjacent, orthogonally oriented nonlinear crystals. The quality and brightness of this source is then dramatically improved through the use of birefringent crystals which compensate for an angle-dependent phase shift. The use of these compensation crystals has allowed measured count rates of two million pairs per second with 97.7% fidelity (with a maximally entangled state) or alternately, ten thousand pairs per second with 99.5% fidelity. By manipulating these entangled states, it is possible to study both how they change and how they can be used. We discuss the theory of state manipulation and the experimental implementation of extremely precise single-qubit operations. To study the operations themselves, we use quantum process tomography to characterize them and have successfully implemented the first experimental realization of ancilla-assisted process tomography. To study decoherence, we implemented the first experimental decoherence-free subspace. By using techniques developed during these investigations, we are able to transform our source of entangled photons into a source of any two-photon polarization state, mixed or pure. Developing new techniques for state creation and manipulation is possible because of simultaneous development in state measurement. In addition to detailing both a theoretical analysis and experimental instructions for state tomography, we experimentally and theoretically compared state tomography with tests of local realism (Bell inequalities) and entanglement witnesses (an entanglement detection technique). In the process, we have measured the largest violations of local realism to date, both statistical (over 2400-sigma) and absolute (S = 2:826 ± 0:005 -- within 0:2% of a maximal violation).
Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.
A causal understanding of a physical theory is vital. They provide profound insights into the implications of the theory and contain the information required to manipulate, not only predict, our surroundings. Unfortunately, one of the most broadly used and successful theories, quantum theory, continues to evade a satisfactory causal description. The progress is hindered by the difficulty of faithfully testing causal explanations in an experimental setting. This thesis presents a novel causal discovery algorithm which allows a direct comparison of a wide variety of causal explanations for experimental data. They include causal influences both classical and quantum mechanical in nature. First we provide relevant background information, predominately on quantum mechanics, quantum optics and statistical inference. Next, we review the framework of classical causality and the connection between a causal assumption and statistical model. We then present a novel causal discovery algorithm for noisy experimental data. Finally, we perform two Bell experiments and apply the newly developed algorithm on the resulting data. \nThe causal discovery algorithm operates on observational data without any interven- tions required. It utilizes the concept of predictive accuracy to assign a score to each causal explanation. This allows the simultaneous consideration of classical and quantum causal theories. In addition, this approach allows the identification of overly complex explanations as these perform poorly with respect to this criterion. \nBoth experiments are implemented using quantum optics. The first Bell experiment has a near maximally entangled shared resource state while the second has a separable resource state. The results indicate that a quantum local causal explanation bests describes the first experiment, whereas a classical local causal explanation is preferred for the second. A super-luminal or super-deterministic theory are sub-optimal for both.