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Decoherence and Beyond - Decoherence and Beyond by Robin...

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Decoherence and Beyond by Robin Jack Blume-Kohout B.A. (Kenyon College) 1998 M.A. (University of California, Berkeley) 2000 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor Raymond Chiao, Chair Doctor Wojciech H. Zurek Professor Birgitta Whaley Professor Daniel Stamper-Kurn Spring 2005
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The dissertation of Robin Jack Blume-Kohout is approved: Chair Date Date Date Date University of California, Berkeley Spring 2005
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Decoherence and Beyond Copyright 2005 by Robin Jack Blume-Kohout
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1 Abstract Decoherence and Beyond by Robin Jack Blume-Kohout Doctor of Philosophy in Physics University of California, Berkeley Professor Raymond Chiao, Chair I investigate the ways in which information about an open quantum system is recorded in its environment. The underlying themes are classicality and its symptom, objectivity . How decoherence leads to redundantly recorded information is of particular importance. Redundancy is introduced as a concrete manifestation of objectivity, and a set of tools for identifying redundancy is presented. Several variants of spin bath and oscillator bath models for decoherence are analyzed in terms of redundancy. Redundant information storage is shown to be a common feature of decoherence models. Predictability and amplification, two related symptoms of classicality, are also explored. I introduce the operator sieve , an improved algorithm for implementing the predictability sieve, and apply it to the problem of connecting redundancy and predictability. This leads to a general theory of information-preserving structures , which unifies pointer bases with decoherence-free sub- spaces/subsystems in an algebraic framework. As a first step in exploring amplification (and its connections with redundancy), a simple analytic model of an unstable environment is solved. I show that a single amplifying degree of freedom can produce more (and faster) decoherence than an bath of infinitely many oscillators.
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2 Professor Raymond Chiao Dissertation Committee Chair
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i To Asher Peres, who I’d like to think would have liked this. 1934 - 2005
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ii Contents List of Figures vi List of Tables ix I Decoherence: Introduction, Implications, Extensions 1 1 Introduction 3 1.1 Background: decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Introduction to objectivity and redundancy . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Overview of original material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.1 Introducing Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2 Redundancy in spin-bath systems . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.3 Redundancy in quantum Brownian motion . . . . . . . . . . . . . . . . . . . 11 1.3.4 Pointer bases and the operator-sieve . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.5 Amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 II Redundancy: a Detailed Exploration 13 2 Introducing Redundancy 15 2.1 Redundancy and its relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 The redundancy programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.2 Computing quantitative redundancy . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.3 Identifying qualitative redundancy . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Characterizing randomly-selected states . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.1 The uniform ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.2 Partial information plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Decoherence and branching states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.1 The branching-state ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.2
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