Secret key distillation across a quantum wiretap channel under restricted eavesdropping

The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Further, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, e.g., to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.Comment: 14 pages, 19 figures. We welcome comments and suggestion

Finite-Block-Length Analysis in Classical and Quantum Information Theory

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects

Bipartite Quantum Interactions: Entangling and Information Processing Abilities

The aim of this thesis is to advance the theory behind quantum information processing tasks, by deriving fundamental limits on bipartite quantum interactions and dynamics, which corresponds to an underlying Hamiltonian that governs the physical transformation of a two-body open quantum system. The goal is to determine entangling abilities of such arbitrary bipartite quantum interactions. Doing so provides fundamental limitations on information processing tasks, including entanglement distillation and secret key generation, over a bipartite quantum network. We also discuss limitations on the entropy change and its rate for dynamics of an open quantum system weakly interacting with the bath. We introduce a measure of non-unitarity to characterize the deviation of a doubly stochastic quantum process from a noiseless evolution. Next, we introduce information processing tasks for secure read-out of digital information encoded in read-only memory devices against adversaries of varying capabilities. The task of reading a memory device involves the identification of an interaction process between probe system, which is in known state, and the memory device. Essentially, the information is stored in the choice of channels, which are noisy quantum processes in general and are chosen from a publicly known set. Hence, it becomes pertinent to securely read memory devices against scrutiny of an adversary. In particular, for a secure read-out task called private reading when a reader is under surveillance of a passive eavesdropper, we have determined upper bounds on its performance. We do so by leveraging the fact that private reading of digital information stored in a memory device can be understood as secret key agreement via a specific kind of bipartite quantum interaction.Comment: PhD Thesis (minor revision). Also available at: https://digitalcommons.lsu.edu/gradschool_dissertations/4717

Physical-Layer Security, Quantum Key Distribution and Post-quantum Cryptography

The growth of data-driven technologies, 5G, and the Internet place enormous pressure on underlying information infrastructure. There exist numerous proposals on how to deal with the possible capacity crunch. However, the security of both optical and wireless networks lags behind reliable and spectrally efficient transmission. Significant achievements have been made recently in the quantum computing arena. Because most conventional cryptography systems rely on computational security, which guarantees the security against an efficient eavesdropper for a limited time, with the advancement in quantum computing this security can be compromised. To solve these problems, various schemes providing perfect/unconditional security have been proposed including physical-layer security (PLS), quantum key distribution (QKD), and post-quantum cryptography. Unfortunately, it is still not clear how to integrate those different proposals with higher level cryptography schemes. So the purpose of the Special Issue entitled “Physical-Layer Security, Quantum Key Distribution and Post-quantum Cryptography” was to integrate these various approaches and enable the next generation of cryptography systems whose security cannot be broken by quantum computers. This book represents the reprint of the papers accepted for publication in the Special Issue

Continuous Variable Quantum Key Distribution over Long Distances

Quantum key distribution (QKD) is fundamentally different from most classical key distribution schemes, such as Diffie-Hellman key exchange, in the sense that no computational complexity assumption is required on the power of adversaries to prove its security. QKD relies on basic laws of quantum physics and it is proven that it can enable highly secure data communication. Such achievements, however, are facing technological problems that have to be resolved in order to provide a viable solution to a large group of customers. While there are discrete-variable QKD schemes, which rely on encoding data in discrete degrees of freedom, such as polarization of single photons, in this thesis, we focus on the continuous-variable QKD (CV-QKD) protocols, in which data is encoded on the quadratures of light. Currently, one of the major drawbacks of CV-QKD is its poor performance at long distances. Nevertheless, such a limitation in CV-QKD can be overcome with the assistance of quantum repeaters that rely on entanglement distillation via noiseless linear amplifiers (NLAs). Such systems can, in principle, offer large secret key rates over long distances. In this thesis, we aim to provide a realistic analysis of a CV-QKD protocol running over quantum scissors (QSs) as realistic NLAs. We will report the obstacles that one could face in realizing CV-QKD in such a scenario. A review of CV-QKD and QS-based NLAs will be given, based on which QS-assisted CV-QKD is proposed. We, particularly, focus on the modelling of the QSs' structure and their effect on the secret key rate aiming to find operational regimes where the performance of the QKD scheme is enhanced. This study paves the way for implementing long-distance CV-QKD protocols that rely on QS/NLA devices over CV quantum repeaters. In this thesis, we also consider and account for a realistic analysis of a CV-QKD protocol with non-Gaussian modulation, which is assisted by the means of QSs. We will show that, while we have to deal with similar obstacles as in the Gaussian modulation, we can potentially improve performance of the non-Gaussian modulation protocol. As an alternative approach to extend the secure distance of CV-QKD protocols, the last part of this thesis is devoted to presenting realistic threat models for satellite QKD, wherein we consider several eavesdropping scenarios by limiting eavesdroppers' access to the trusted ground and/or satellite stations. In such scenarios, the eavesdropper has only limited access to the sender and/or receiver stations. For example, we will explore the case where an eavesdropper can only receive an attenuated version of the transmitted signals. As well, we will focus on the case where Eve's signals would reach the receiver via a lossy channel inaccessible to the eavesdropper. We show that, in the case of both Gaussian and non-Gaussian protocols, this limitation would allow trusted parties to achieve higher key rates than what can be achieved when unrestricted eavesdropping is possible