Doctor of Philosophy (PhD)
Physics and Astronomy
The formalism of covariant quantum theory, introduced by Reisenberger and Rovelli, casts the description of quantum states and evolution into a framework compatible with the principles of general relativity. The leap to this covariant formalism, however, outstripped the standard interpretation used to connect quantum theory to experimental predictions, leaving the predictions of the theory ambiguous. In particular, the absence of a pre-defined time variable or background causal structure resulted in an ``order of projections" ambiguity, in which the usual rule for multiple-measurement probabilities (obtained by time-ordered projections) is not defined. Equally troublesome, the probability postulate of Reisenberger and Rovelli fails to reproduce the Born interpretation for the case of simple quantum mechanical systems. Here, we develop an alternative quantum measurement formalism, based on basic principles of quantum information. After reviewing how this can be done in the context of the traditional formulation of quantum mechanics and noting its implications for the quantum measurement problem, we find that this approach can be generalized to the covariant setting, where it essentially solves the correspondence problems of covariant quantum theory. We show explicit agreement with the Born interpretation of standard quantum mechanics in the context of simple systems. We also demonstrate the origin of the quantum mechanical arrow of time within our framework, and use this to solve the order of projections ambiguity. In addition to compatibility with general covariance, we show that our framework has other attractive and satisfying features - it is fully unitary, realist, and self-contained. The full unitarity of the formalism in the presence of measurements allows us to invoke time-reversal symmetry to obtain new predictions closely related to the quantum Zeno effect.
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Release the entire work immediately for access worldwide.
Olson, Stephan Jay, "Generally covariant quantum information" (2008). LSU Doctoral Dissertations. 3715.