We describe various quantum communication protocols, using either Gaussian states (for continuous-variable quantum cryptography) or non-Gaussian states (for various applications, including non-deterministic noiseless amplification). Perspectives for deterministic vs non-deterministic quantum information processing will be discussed.
This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its structural mathematical description makes them much more amenable than any other CV system. Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control. Nevertheless, it is known that in spite of their exceptional role within the space of all Continuous Variable states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus non-Gaussian states emerge as potentially good candidates for communication and computation purposes.
The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
In this thesis we consider quantum communication as realised in the continuous variable quantum optical regime. The work presented includes results concerning quantum communication applications, such as entanglement distillation and quantum key distributions, as well as fundamental questions regarding measurement uncertainty and the boundary between classical and quantum correlations. In the first part of the thesis we investigate various protocols in which one engages in a trade-off between determinism and the quality of quantum correlations. In discrete variable quantum optics non-determinism is ubiquitous, with photon sources, detectors and various gates commonly operating probabilistically. In the continuous variable regime one has access to many quantum states and operations, including exotic effects such as entanglement, in a fully deterministic fashion and one might regard giving up this feature as highly undesirable. However it has been discovered that certain vital tasks such as entanglement distillation, indispensable for large scale quantum information networks, cannot be realised deterministically. We address precisely these limitations, firstly by conducting the most general analysis to date of a non-deterministic but heralded quantum amplifier that can circumvent the standard quantum limits, and distill Gaussian entanglement. We then analyse the security of long standing technique in continuous variable quantum key distribution, known as post-selection, which again allows the distillation of higher quality correlations. We provide a complete security proof in the asymptotic limit and show that there is in fact an relationship between this method and the noiseless amplifier. Furthermore, the protocol allows secure key to be generated for channel parameters where all previous CVQKD protocols fail. Thirdly we consider this equivalence between post-selection and heralded operations more generally, and conduct a detailed analysis of the post-selection based emulation of the noiseless amplifier. Turning to more fundamental issues, we consider links between several recently proposed entropic measures of quantum correlations and their potential operational links to continuous variable quantum key distribution. Finally we consider entropic uncertainty relations for continuous variables on infinite dimensional Hilbert spaces and apply these to one-sided device independent continuous variable quantum key distribution protocols.n
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrodinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
We present a very brief overview of entanglement swapping as it relates to continuous-variable quantum information. The technical background required is discussed and the natural link to quantum teleportation is established before discussing the nature of Gaussian entanglement swapping. The limitations of Gaussian swapping are introduced, along with the general applications of swapping in the context of to quantum communication and entanglement distribution. In light of this, we briefly summarize a collection of entanglement swapping schemes which incorporate a non-Gaussian ingredient and the benefits of such schemes are noted. Finally, we motivate the need to further study and develop such schemes by highlighting requirements of a continuous-variable repeater.
Quantum information processing with continuous variables is a paradigm that has attracted a growing interest over the past years, partly as a consequence of the prospects for high-rate quantum communication systems based on standard optical telecommunication components. In this overview article, we introduce the concept of quantum continuous variables in optics and then turn to the fundamental impossibility of cloning continuous-variable light states, a result that lies at the heart of quantum key distribution. Then we present state-of-the-art quantum key distribution systems relying on continuous variables, focusing mainly on the protocols using Gaussian-modulated coherent light states and emphasizing the current experimental demonstration of these systems. Finally, we briefly review recent security proofs of these cryptographic protocols.