In quantum information and communication, optical schemes provide simple and intuitive experimental implementations. Of particular importance is quantum state preparation. In this thesis, the creation of polarisation entanglement using a particular class of optical circuits is studied. I give a mathematical description of this class of circuits in terms of Hermite polynomials. In this context, single photon resolution and single photon sensitivity detectors are discussed and compared with detector cascading. In addition, I study applications of state preparation such as quantum teleportation and quantum lithography.
In quantum information and communication, optical schemes provide simple and intuitive experimental implementations. Of particular importance is quantum state preparation. In this thesis, the creation of polarisation entanglement using a particular class of optical circuits is studied. I give a mathematical description of this class of circuits in terms of Hermite polynomials. In this context, single photon resolution and single photon sensitivity detectors are discussed and compared with detector cascading. In addition, I study applications of state preparation such as quantum teleportation and quantum lithography.
We study the use of detection devices in entanglement-based state preparation. In particular we consider optical detection devices such as single-photon sensitivity detectors, single-photon resolution detectors, and detector cascades (with an emphasis on the performance of realistic detectors). We develop an extensive theory for the use of these devices. In entanglement-based state preparation we perform measurements on subsystems, and we therefore need precise bounds on the distinguishability of these measurements (this is fundamentally different from, e.g., tomography, where an ensemble of identical states is used to determine probability distributions, etc.). To this end, we introduce the confidence of preparation, which may also be used to quantify the performance of detection devices in entanglement-based preparation. We give a general expression for detector cascades of arbitrary size for the detection up to two photons. We show that, contrary to the general belief, cascading does not give a practical advantage over detectors with single-photon resolution in entanglement-based state preparation.
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
Quantum information theory has revolutionized the way in which information is processed using quantum resources such as entangled states, local operations and classical communications. Two important protocols in quantum communications are quantum teleportation and remote state preparation. In quantum teleportation neither the sender nor the receiver know the identity of a state. In remote state preparation the sender knows the state which is to be remotely prepared without ever physically sending the object or the complete classical description of it. Using one unit of entanglement and one classical bit Alice can remotely prepare a photon (from special ensemble) of her choice at Bob's laboratory. In remote state measurement Alice asks Bob to simulate any single particle measurement statistics on an arbitrary photon. In this talk we will present these ideas and discuss the latest developments and future open problems.
Quantum optics offers a huge variety of exciting phenomena. Many of them are still in their infancy and especially when it comes to implementing devices using these effects for more than a proof of principle demonstration still many things have to be investigated and understood. In this thesis I discuss the role of correlations in some areas of quantum optics and in some cases compare it to classical optics. Four papers form the core of the thesis. In the first paper, I propose a new measure for entanglement. This measure is based on correlations between two states. I show, how this measure relates to another measure, the concurrence. It turns out that the measure is a bijective map of the concurrence for a pure state of two qubits. I motivate why the new measure is useful if one wants to implement it experimentally. I discuss its behaviour for the case of two qubits and show its properties when dealing with pure and with mixed states. The second paper extends the result of the first one to the case where one has higher-dimensional states than qubits. In the third paper I look at phase super-resolution. I show that it can be interpreted as a purely classical effect and I analyse what is needed and what is not needed to achieve it. Specifically, I show that quantum correlations in terms of entanglement is not needed to demonstrate phase super-resolution. By doing so I propose how one could achieve arbitrarily high phase super-resolution. Finally, the last paper looks at the efficiency of quantum lithography and quantum imaging. It shows, that some basic assumptions in the original proposals of quantum lithography seems unfounded and that, as a consequence, the efficiency is poor. I give formulæ for the explicit scaling behaviour when changing the number of photons in a mode or when changing the number of pixels. The effect of the results on the future of quantum lithography is discussed as well.
Quantum state preparation is important for quantum information processing. In particular, in optical quantum computing with continuous variables, non-Gaussian states are needed for universal operation and error correction. Optical non-Gaussian states are usually generated by heralding schemes using photon detectors. In previous experiments, the temporal resolution of the photon detectors was sufficiently high relative to the time width of the quantum state, so that the conventional theory of non-Gaussian state preparation treated the detector's temporal resolution as negligible. However, when using various photon detectors, including photon-number-resolving detectors, the temporal resolution is non-negligible. In this paper, we extend the conventional theory of quantum state preparation using photon detectors to the finite-temporal-resolution regime, analyze the cases of single-photon and two-photon preparation as examples, and find that the generated states are characterized by the dimensionless parameter B, defined as the product of the temporal resolution of the detectors $\mathrm{\ensuremath{\Delta}}t$ and the bandwidth of the light source $\mathrm{\ensuremath{\Delta}}f$. Based on the results, $B\ensuremath{\sim}0.1$ is required to keep the purity and fidelity of the generated quantum states high.
Measurements on states of light underpins the entire fields of classical and quantum optics. Without measurement we are unable to gain any information about the light we are studying or about the processes it has undergone. The property of the density matrix of light prior to measurement that we want to measure also relies heavily on the measurement technique we employ. We can use a single-photon detector to measure the particle nature of light--the photon--the discrete quanta of the electromagnetic field. We can conversely measure the wave nature of the light field by making phase-sensitive measurements. In this thesis, we shall explore some advanced implementations and applications of these measurement schemes. First, we shall focus on a specific type of single-photon detector: the Superconducting-Nanowire Single-Photon Detector. We will first consider the integration of these detectors on optical waveguides, and discuss their optical characterisation. Then we will consider a practical application of these detectors by investigating a method to perform broadband spectroscopy with a single detector. We shall then progress to phase-sensitive measurements, and consider the intermediate regime between measuring the wave-like and particle-like nature of light. First we will perform a fundamental investigation of the transition between both measurement regimes. We will see how varying the phase reference itself allows us to tune between both regimes. Following this we will discuss an application of this intermediate regime, by considering an experimental setup to perform state tomography with a weak phase reference. The final consideration of this thesis will be a theoretical benchmarking scheme for a practical application of quantum optics. The manipulation of certain quantum states of light followed by a photon-number measurement can have practical applications in a variety of fields, and therefore validating the results is of extreme importance. On this final topic, we will discuss an experimentally friendly technique to benchmark the output of such measurements by considering smaller subsystems, and the practical requirements of this technique.