This thesis encompasses a collection of four pieces of work on wave-particle duality, weak-value-assisted tomography, high-dimensional quantum key distribution, and phase-only holograms. In the work on duality, we derive a novel duality relation, and we sketch a thought experiment that leads to an apparent violation of the duality principle. In the project on tomography, we perform a state determination procedure with weak values, and we study the accuracy of the method. In the quantum cryptography project, we optimize an experimental implementation of a quantum cryptography system where two parties share information with the orbital angular momentum degree of freedom of entangled photon pairs. Finally, in the work on holography, we establish the exact solution to the encryption of a phase-only hologram, and experimentally demonstrate its application to spatial light modulators. The four projects provide improvements on measurement procedures in applied and fundamental quantum mechanics.
This thesis encompasses a collection of four pieces of work on wave-particle duality, weak-value-assisted tomography, high-dimensional quantum key distribution, and phase-only holograms. In the work on duality, we derive a novel duality relation, and we sketch a thought experiment that leads to an apparent violation of the duality principle. In the project on tomography, we perform a state determination procedure with weak values, and we study the accuracy of the method. In the quantum cryptography project, we optimize an experimental implementation of a quantum cryptography system where two parties share information with the orbital angular momentum degree of freedom of entangled photon pairs. Finally, in the work on holography, we establish the exact solution to the encryption of a phase-only hologram, and experimentally demonstrate its application to spatial light modulators. The four projects provide improvements on measurement procedures in applied and fundamental quantum mechanics.
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
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.
Abstract Cryptography plays an important role in information security, which is widely applied in the various fields of society. Quantum cryptography has shown its great advantages in information security compared with the classical one. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the well accepted success of the QKD, the development of quantum encryption is rather limited because of the difficulties of building up algorithms and the constructing the practical quantum computers. Here we propose a new scheme of quantum encryption based on high-dimensional entanglement holography. Firstly, we experimentally realize the quantum holography based on the high-dimensional orbital angular momentum (OAM) entanglement. Then, OAM-selective holographic scheme for quantum encryption is proposed and demonstrated. Our results show that introducing quantum entangled state into OAM holography makes the OAM holography possess infinite information channels and the transmission of information be absolute security in principle. Furthermore, decryption in the presence of strong noise is achieved. Our work opens up a new way to realize quantum information security.
This thesis presents the results of a series of four photonic experiments on the topic of quantum measurement. The first two experiments relate to quantum metrology, and the use of quantum states to increase the precision of measurements beyond what is possible with classical systems; first to detect and characterize decoherence, and then in the context of quantum imaging. The third experiment studies a fundamental question in quantum mechanics: "How much must a quantum system be disturbed by a measurement?". We use weak measurement to confirm a recent theoretical result, showing that if a particle's state is already sufficiently uncertain we can perform a measurement with very little disturbance -- contrary to common explanations of Heisenberg's uncertainty principle. The fourth experiment falls in the category of quantum computation. In quantum mechanics having multiple copies of an identical system allows us to extract more information than we can extract from a single copy (since quantum mechanics allows each system to be measured only once before collapsing). We present and experimentally implement a quantum algorithm to compress all of the "extractable information" present in an ensemble of identical copies of quantum bits into exponentially fewer quantum bits. The research presented here samples from a variety of topics in quantum information, showing in several contexts how fascinating quantum effects can be exploited to gain a "quantum enhancement".To enable these experiments two sources of entangled photons were built, and "hybrid" quantum systems (encoding information in multiple degrees of freedom of a photon) were used to implement quantum circuits. This thesis will present the details of one of these sources (a novel and practical source of entangled N00N states), which was used in a four-photon quantum metrology experiment. The other, more standard, source of polarization-entangled photon pairs will only briefly be reviewed to leave room for the discussion of hybrid quantum logic.
Quantum entanglement is a fundamental trait of quantum mechanics that causes the information about the properties of two (or more) objects to be inextricably linked. When a measurement on one of the objects is performed, the state of the other object is immediately altered, even when these objects are separated at arbitrary distances. In this thesis, we explore the rich properties of entanglement in a high-dimensional mode space. Experimentally, we have implemented the high dimensionality by use of the orbital-angular-momentum degree of freedom of entangled photon pairs. The emphasis is on the question how to quantify the dimensionality of the entanglement as measured in an experiment. We introduce the Shannon dimensionality as a useful quantifier of measured entanglement. Furthermore, we discuss various production methods of optical phase plates, which we use to manipulate the orbital-angular-momentum states of light. Finally, we present an experimental feasibility study on the potential of orbital-angular-momentum entanglement for free-space quantum communication through the atmosphere
This thesis consists of four research papers and an introduction covering the most important concepts appearing in the papers. The papers deal with applications of gauge/gravity dualities in the study of various physical quantities and systems. Gauge/gravity dualities are equivalences between certain quantum field theories and classical theories of gravity. These dualities can be used as computational tools in a wide range of applications across different fields of physics, and as such they have garnered much attention in the last two decades. The great promise of these new tools is the ability to tackle difficult problems in strongly interacting quantum field theories by translating them to problems in classical gravity, where progress is much easier to make. Quantum information theory studies the information contained in quantum systems. Entanglement is the fundamental property of quantum mechanics that sets it apart from classical theories of physics. Entanglement is commonly quantified by entanglement entropy, a quantity which is difficult to compute in interacting quantum field theories. Gauge/gravity dualities provide a practical way for computing the entanglement entropy via the Ryu-Takayanagi formula. The primary focus of this thesis is to use this formula for computing various entanglement measures in strongly interacting quantum field theories via their gravity duals. The purpose of this thesis is to introduce quantum information theory concepts that have been important in our research. When applicable, quantities of interest are first introduced in the classical setting in order to build intuition about their behaviour. Quantum properties of entanglement measures are discussed in detail, along with their holographic counterparts, and remarks are made concerning their applications.