Which verification qubits perform best for secure communication in noisy channel?

In secure quantum communication protocols, a set of single qubits prepared using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$) entangled states of a particular form are usually used to form a verification string which is subsequently used to detect traces of eavesdropping. The qubits that form a verification string are referred to as decoy qubits, and there exists a large set of different quantum states that can be used as decoy qubits. In the absence of noise, any choice of decoy qubits provides equivalent security. In this paper, we examine such equivalence for noisy environment (e.g., in amplitude damping, phase damping, collective dephasing and collective rotation noise channels) by comparing the decoy-qubit assisted schemes of secure quantum communication that use single qubit states as decoy qubits with the schemes that use entangled states as decoy qubits. Our study reveals that the single qubit assisted scheme perform better in some noisy environments, while some entangled qubits assisted schemes perform better in other noisy environments. Specifically, single qubits assisted schemes perform better in amplitude damping and phase damping noisy channels, whereas a few Bell-state-based decoy schemes are found to perform better in the presence of the collective noise. Thus, if the kind of noise present in a communication channel (i.e., the characteristics of the channel) is known or measured, then the present study can provide the best choice of decoy qubits required for implementation of schemes of secure quantum communication through that channel.Comment: 11 pages, 4 figure

Quantum entanglement

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended) presentation, updated references, minor changes, submitted to Rev. Mod. Phys

Gaussian Quantum Information

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.Comment: 51 pages, 7 figures, submitted to Reviews of Modern Physic

QKD and high-speed classical data hybrid metropolitan network

Quantum Key Distribution (QKD) is currently receiving much attention as it provides a secure source of encryption keys. Discrete-Variable QKD (DV-QKD) is possible for single photon transmission in QKD to-coexist with and encode classical wavelength division multiplexed (WDM) data with appropriate system design. Nevertheless, previous QKD field trials adopted either or both of key relay via trusted nodes and transparent link via optical switching. The former requires guaranteed physical security of the relay nodes, but can expand key distribution distance arbitrarily. The latter can realize key establishment for more users with less complexity of key management over an untrusted network. To realise the adaption of the QKD system for future high speed and long distance metropolitan world exploitation at lower cost, there has to be investigations on existing fibre infrastructures. Prior to this work, previous researches over similar distances feature extremely low secure key rates. For example, the Swiss Quantum Network between three sites displayed secure bit rates of 2.5 kbps at a fibre length of 17km. Quantum Key distribution within the 25km Cambridge Quantum Network have demonstrated the highest long-term secure key rates yet demonstrated in a field trial of at least 2.5Mb/s which is the fastest and much higher than 0.8 kbps which was reached over the similar channel loss field trial up to date. Additional field trials have been performed on the UK Quantum Network using a 66km path having 16dB loss. Combined wavelength division multiplexed 2 x 100 Gb/s traffic encrypted using QKD co-existing on the same fibres has operated for several months, with a long-term key rate of 80kb/s that is also faster than any other similar long-term QKD trial systems. In addition to this advanced commercial QKD system, there have been secure key rate analysis comparisons between laboratory fibre coils and practical field trials more than field trials only conducted before.These comparisons help to identify factors that limit future QKD network scale in both quantity and quality aspects. Also, the limit for the highest secure key rate at longest fibre length QKD in the multiplexing environment is discussed and determined in this research thesis. Nevertheless, in this thesis, improvements have been made to minimise the corresponding negative effects by investigations on the dependence of temperature have been done in order to ensure system operation environment effects. It was found from the trial results that there exists a relationship between temperature and secure key rate and further study has been done to evaluate the system sensitivity to operating temperature. Although the conventional DV-QKD system, original BB84 coding scheme, was designed to exploit the quantum properties of single photon polarization states, the trial equipment operates based upon the phase coding schemes. These coding schemes are based on the properties of interferometers and the coding is implemented by changing the relative optical path lengths or phase between the internal arms of the interferometer, while in the real transmission environment, temperature or polarization variation happens unpredictably. The existing polarisation controllers operate at relative low speed align within the interferometer, which slows to operation environment such as a punch to fibre causing phase difference. Therefore, in this project, there has been an improvement in the QKD-WDM system performance by adding an external polarization controller to minimize the Raman noise and increase the secure key rate at the longest fibre length up to date. In Summary, transmitting quantum keys over a coil of fibre in the lab differs a lot from actually putting it in the ground. This work contrasts the world fastest QKD system at the longest distance in field trials with lab fibre reels and then characterises and identifies two of the key factors, temperature and polarizations, influencing performance in practical wavelength-multiplexed secure communication systems. This is a significant step towards the coexistence of the quantum and conventional data channels on the same fibre for metropolitan networks and paves a way for an information-secure communication infrastructure

Applications of coherent classical communication and the Schur transform to quantum information theory

Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory--coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half.Comment: 176 pages. Chapters 1 and 4 are a slightly older version of quant-ph/0512015. Chapter 2 is quant-ph/0205057 plus unpublished extensions (slightly outdated by quant-ph/0511219) and chapter 3 is quant-ph/0307091, quant-ph/0412126 and change. Chapters 5-8 are based on quant-ph/0407082, but go much furthe

Pathway to the Square Kilometre Array - The German White Paper -

The Square Kilometre Array (SKA) is the most ambitious radio telescope ever planned. With a collecting area of about a square kilometre, the SKA will be far superior in sensitivity and observing speed to all current radio facilities. The scientific capability promised by the SKA and its technological challenges provide an ideal base for interdisciplinary research, technology transfer, and collaboration between universities, research centres and industry. The SKA in the radio regime and the European Extreme Large Telescope (E-ELT) in the optical band are on the roadmap of the European Strategy Forum for Research Infrastructures (ESFRI) and have been recognised as the essential facilities for European research in astronomy. This "White Paper" outlines the German science and R&D interests in the SKA project and will provide the basis for future funding applications to secure German involvement in the Square Kilometre Array.Comment: Editors: H. R. Kl\"ockner, M. Kramer, H. Falcke, D.J. Schwarz, A. Eckart, G. Kauffmann, A. Zensus; 150 pages (low resolution- and colour-scale images), published in July 2012, language English (including a foreword and an executive summary in German), the original file is available via the MPIfR homepag

Intriguing Properties and Applications of Functional Magnetic Materials

Functional magnetic materials, also called the smart materials of the future, are a group of materials having important and interesting physical properties, which can be affected when an external magnetic field is applied. They are intriguing models that have a strong impact on improving different technologies. Their magnetic response to an external magnetic field can be represented as paramagnetic, diamagnetic, ferromagnetic, or antiferromagnetic. Compared with bulk materials, they show uncommon magnetic behavior as a result of their surface/interface effects, electronic charge transfer, and magnetic interactions. They can be used in different vital applications like data storage systems, refrigeration, magnetic recording, and medical studies. In this chapter, essential attractive magnetic properties that are relevant to different applications will be explained