Quantum Correlations, Data Hiding, and Quantum Many-body Systems

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Two or more quantum systems can be correlated in a way that defies any classical explanation. In the last twenty years, it has emerged that this kind of quantum correlations, termed entanglement, has a distinguished role in information processing. It turns out that entangled quantum systems can be harnessed to transmit, store, and manipulate information in a more efficient and secure manner than possible in the realm of classical physics. From a different perspective, the existence of entanglement in quantum theory also has dramatic consequences to our ability to simulate quantum many-body systems: It is widely believed that it is impossible to simulate efficiently in a classical computer the dynamics of quantum many-body systems. While this is a major problem when studying such systems, e.g. in the condensed matter context, it naturally leads to the idea of a quantum computer, in which controlled quantum systems are employed to perform computation in a more efficient way than possible by classical means. The field of quantum information and computation is concerned with the usefulness and limitations of quantum-mechanical systems to computation and information processing. The objective of the research is to make progress on several outstanding theoretical questions of quantum information science.In the first theme one will address questions that would represent key progress to our understanding of quantum entanglement and its use in quantum information transmission. The first topic is focused on understanding the inherent irreversibility in the manipulation of entanglement. The second topic, in turn, seeks to achieve a better understanding of the non-additivity of quantum information in quantum communication channels. The second theme will focus on quantum data hiding, correlations that are not accessible by restricted measurements (e.g. local ones), and in particular how one can address several current challenges in quantum information science by pursuing an in-depth understanding of data hiding in quantum systems. The research will focus on three topics related to quantum data hiding. The first two are related to the difficulties brought by data hiding states to two outstanding open problems in quantum information theory - the task of deciding if a state is entangled and the establishment of area laws for gapped local Hamiltonians -, together with proposals for overcoming them. The third addresses the question of generating quantum data hiding states by very simple procedures, such as constant depth quantum circuits, and its impact to the problem of understanding equilibration of quantum systems from first principlesThe final theme is concerned with quantum hamiltonian complexity, an exciting new area linking condensed matter physics and quantum many-body theory to computational complexity theory and quantum computation. The research will address two topics in this direction. The first concerns the possibility of performing quantum computation by cooling down physical systems. The second is concerned with determining the computational complexity of estimating properties of thermal states of local models.Together these 3 themes will enable us to widen our understanding of quantum correlations, quantum many-body systems, and the use of quantum-mechanical systems for information processing.