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The theory of decoherence aims to explain how macroscopic quantum objects become effectively classical. Understanding this process could help in the search for the quantum theory underlying gravity, and suggest new schemes for preserving the coherence of technological quantum devices. The process of decoherence is best understood in terms of information flow within a quantum system, and between the system and its environment. We develop a novel way of characterizing this information, and give a sufficient condition for its classicality. These results generalize previous models of decoherence, clarify the process by which a phase-space based on non-commutative quantum variables can emerge, and provide a possible explanation for the universality of the phenomenon of decoherence. In addition, the tools developed in this approach generalize the theory of quantum error correction to infinite-dimensional Hilbert spaces. We characterize the nature of the information preserved by a quantum channel by the observables which exist in its image (in the Heisenberg picture). The sharp observables preserved by a channel form an operator algebra which can be characterized in terms of the channel's elements. The effect of the channel on these observables can be reversed by another physical transformation. These results generalize the theory of quantum error correction to codes characterized by arbitrary von Neumann algebras, which can represent hybrid quantum-classical information, continuous variable systems, or certain quantum field theories. The preserved unsharp observables (positive operator-valued measures) allow for a finer characterization of the information preserved by a channel. We show that the only type of information which can be duplicated arbitrarily many times consists of coarse-grainings of a single POVM. Based on these results, we propose a model of decoherence which can account for the emergence of a realistic classical phase-space. This model supports the view that the quantum-classical correspondence is given by a quantum-to-classical channel, which is another way of representing a POVM.

The theory of decoherence aims to explain how macroscopic quantum objects become effectively classical. Understanding this process could help in the search for the quantum theory underlying gravity, and suggest new schemes for preserving the coherence of technological quantum devices. The process of decoherence is best understood in terms of information flow within a quantum system, and between the system and its environment. We develop a novel way of characterizing this information, and give a sufficient condition for its classicality. These results generalize previous models of decoherence, clarify the process by which a phase-space based on non-commutative quantum variables can emerge, and provide a possible explanation for the universality of the phenomenon of decoherence. In addition, the tools developed in this approach generalize the theory of quantum error correction to infinite-dimensional Hilbert spaces. We characterize the nature of the information preserved by a quantum channel by the observables which exist in its image (in the Heisenberg picture). The sharp observables preserved by a channel form an operator algebra which can be characterized in terms of the channel's elements. The effect of the channel on these observables can be reversed by another physical transformation. These results generalize the theory of quantum error correction to codes characterized by arbitrary von Neumann algebras, which can represent hybrid quantum-classical information, continuous variable systems, or certain quantum field theories. The preserved unsharp observables (positive operator-valued measures) allow for a finer characterization of the information preserved by a channel. We show that the only type of information which can be duplicated arbitrarily many times consists of coarse-grainings of a single POVM. Based on these results, we propose a model of decoherence which can account for the emergence of a realistic classical phase-space. This model supports the view that the quantum-classical correspondence is given by a quantum-to-classical channel, which is another way of representing a POVM.

Since the synthesis of Mn12, which can be regarded as the birth of the class of magnetic molecules, many different molecules of various sizes and structures have been produced. The magnetic nature of these molecules originates from a number of paramagnetic ions, whose unpaired electrons form collective angular momenta, referred to as spins. The interaction between these spins can often be described in the Heisenberg model. In this work, we use the rotational band model to predict the energy spectrum of the giant Keplerate {Mo72Fe30}. Based on the approximate energy spectrum, we simulate the cross-section for inelastic neutron scattering, and the results are compared to experimental data. The successful application of our approach substantiates the validity of the rotational band model. Furthermore, magnetic molecules can serve as an example for studying general questions of quantum mechanics. Since chemistry now allows the preparation of magnetic molecules with various spin quantum numbers, this class of materials can be utilized for studying the relations between classical and quantum regime. Due to the correspondence principle, a quantum spin system can be described exactly by classical physics for an infinitely large spin quantum number s. However, the question remains for which quantum numbers s a classical calculation yields a reasonable approximation. Our approach in this work is to develop a converging scheme that adds systematic quantum corrections to the classical density of states for Heisenberg spin systems. To this end, we establish a correspondence of the classical density of states and the quantum spectrum by means of spin-coherent states. The algorithm presented here allows the analysis of how the classical limit is approached, which gives general criteria for the similarity of the classical density of states to the quantum spectrum.