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Title: Entanglement theory and the quantum simulation of many-body physics
Author: Brandao, Fernando G. S. L.
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2008
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Abstract:
Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum mechanics has changed in an equal dramatic manner our understanding of information processing and computation. On one hand, the fundamental properties of quantum systems can be harnessed to transmit, store, and manipulate information in a much more efficient and secure way than possible in the realm of classical physics. On the other hand, the development of systematic procedures to manipulate systems of a large number of particles in the quantum regime, crucial to the implementation of quantum based information processing, has triggered new possibilities in the exploration of quantum many-body physics and related areas. In this thesis, we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement, intrinsically quantum correlations of key importance in quantum information theory, and the exploration of the use of controlled quantum systems to the computation and simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement. In this setting we show how the landscape of entanglement conversion is reduced to the simplest situation possible: one unique measure completely specifying which transformations are achievable. This framework has remarkable connections with the foundations of thermodynamics, which we present and explore. On the way to establish our main result, we develop new techniques that are of interest on their own. First, we extend quantum Stein's Lemma, characterizing optimal rates in state discrimination, to the case where the alternative hypothesis might vary over particular sets of possibly correlated (non-LLd) states. Second, we show how recent advances in quantum de Finetti type theorems can be employed to decide when the entanglement contained in non-LLd. sequences of states is distillable by local operations and classical communication. In the second part we discuss the usefulness of a quantum computer to the determination of properties of many-body systems. Our first result is a new quantum procedure, based on the phase estimation quantum algorithm, to calculate additive approximations to partition functions and spectrum densities of quantum local Hamiltonians. We give convincing evidence that quantum computation is superior to classical in solving both problems by showing that they are complete for the class of problems efficiently solved in the one-c1ean-qubit model of quantum computation, which is believe to contain classically hard problems. We then present a negative result on the usefulness of quantum computers and prove that the determination of the ground state energy of local quantum Hamiltonians, with the promise that the gap is larger than an inverse polynomial in the number of sites, is hard for the class QCMA, which is believed to contain intractable problems even for quantum computation. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. Based on recent experimental developments on cavity quantum electrodynamics, more specifically on the fabrication of arrays of interacting micro-cavities and on their coupling to atomic-like structures in several physical set-ups, we propose and analyse the realization of paradigmatic condensed matter models in such systems, such as the Bose-Hubbard and the anisotropic Heisenberg models. We present· promising properties of such coupled-cavity arrays as simulators of quantum many-body physics, such as the full addressability of individual sites and the access to inhomogeneous models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.491112  DOI: Not available
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