Foundations of quantum cryptography for distribution of secret keys. Quantum cryptographic systems have the advantage of mathematically provable security and privacy, addressing security threats to communications as information and communications technologies proliferate. This project aims to quantify a quantum channel's capability for secure communications. This quantity provides the ultimate limit to benchmark practical quantum key distribution protocols for their performance. This will signif ....Foundations of quantum cryptography for distribution of secret keys. Quantum cryptographic systems have the advantage of mathematically provable security and privacy, addressing security threats to communications as information and communications technologies proliferate. This project aims to quantify a quantum channel's capability for secure communications. This quantity provides the ultimate limit to benchmark practical quantum key distribution protocols for their performance. This will significantly advance the theory of quantum cryptography and knowledge of the fundamental resource of secret keys. It is expected to have immediate application for the classical security of existing (non-quantum) communication devices, and benefit security, military, government, industry, individuals, and the community.Read moreRead less
Quantum effects in zero-error communication. This project will establish a systematic quantum zero-error information theory to build highly reliable quantum communications networks. This innovative, breakthrough technology will advance research into the physical realisation of quantum communication. It has global implications and will promote Australia's position in this new research field.
A mathematical foundation and novel solutions for highly secure communications. This project will deliver novel solutions to security and privacy in communication networks by exploring the power of quantum information with mathematical tools from operator stuctures. It will significantly advance our knowledge about quantum communication, with expected benefits on Australian social, economic and even military security.
Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as we ....Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as well as to viable paths towards the unknown theory that interpolates them. This project contributes to these developments by adapting and developing sophisticated technical tools and insights from integrable models to shed light on that unknown theory that transcends the gauge/string gap. Read moreRead less
Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation ....Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation functions, advances in the theory of topological vertices and the related representation theory, and new solutions of the Yang-Baxter equations. This should provide benefits that include a better understanding of two-dimensional integrable models and their deep connections with topological strings.Read moreRead less
Mathematical structure of the quantum Rabi model. This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the ....Mathematical structure of the quantum Rabi model. This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the building block of quantum information technologies, and so could realise quantum algorithms and quantum computations.Read moreRead less
Representation theory of diagram algebras and logarithmic conformal field theory. Generalized models of polymers and percolation are notoriously difficult to handle mathematically, but can be described and solved using diagram algebras and logarithmic conformal field theory. Potential applications include polymer-like materials, filtering of drinking water, spatial spread of epidemics and bushfires, and tertiary recovery of oil.
Quantum steering, nonlocality and foundations. This project aims at answering foundational questions that will help further our understanding of quantum mechanics---a scientific discipline with proven track record of technological output of great impact in modern society and a huge potential for future developments such as quantum computation and communication. There is a global trend towards interest in quantum foundations, and Australia is already a world leader in the closely related fields o ....Quantum steering, nonlocality and foundations. This project aims at answering foundational questions that will help further our understanding of quantum mechanics---a scientific discipline with proven track record of technological output of great impact in modern society and a huge potential for future developments such as quantum computation and communication. There is a global trend towards interest in quantum foundations, and Australia is already a world leader in the closely related fields of quantum information and quantum-atom optics. Funding of this project will help strengthen and consolidate Australia's position as a world leader in the foundations of quantum mechanics.Read moreRead less
Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Canonical quantisation for classical integrable equations. This project is in the area of fundamental, enabling science. Integrable systems, both classical and quantum, arise as certain classes of dynamical universality in various problems of pure and applied mathematics and in physics. The project will significantly deepen our understanding of cross-relations between geometry and integrable systems.