Quantum estimation for gravitation and quantum information with acceleration

Downes, Tony Gregory (2011). Quantum estimation for gravitation and quantum information with acceleration PhD Thesis, School of Mathematics & Physics, The University of Queensland.

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Author Downes, Tony Gregory
Thesis Title Quantum estimation for gravitation and quantum information with acceleration
School, Centre or Institute School of Mathematics & Physics
Institution The University of Queensland
Publication date 2011
Thesis type PhD Thesis
Supervisor Gerard Milburn
Tim Ralph
Total pages 90
Total colour pages 4
Total black and white pages 86
Language eng
Subjects 020603 Quantum Information, Computation and Communication
020602 Field Theory and String Theory
020105 General Relativity and Gravitational Waves
Abstract/Summary In this thesis we shall apply techniques from quantum information theory to the problem of measuring the structure of spacetime or equivalently measuring the gravitational field. In turn we will also look at how acceleration may effect quantum information techniques for processing and transmitting information. Measuring the structure of spacetime is a slight abuse of terminology as spacetime structure is not directly observable. We will be investigating the estimation of spacetime structure by making measurements on quantum systems which depend on the spacetime background. The structure of spacetime and the gravitational field will be treated in accordance with Einstein's general theory of relativity. This is currently the most accurately tested classical theory for gravity. It is widely believed that fundamentally, gravity should be treated within the framework of quantum mechanics, just like the other forces of nature. This is yet to be seen experimentally and a theory capable of falsifiable predictions is yet to be found. In this thesis we shall focus on the effects of gravity at the classical level, however we shall treat matter and non-gravitational energy using quantum mechanics. When looking at how gravity effects quantum information we will specifically be focusing on the simple case of acceleration, yet we shall treat it in this relativistic spacetime context. Knowing the structure of spacetime in general relativity amounts to knowing an object called the metric tensor. This object contains all the information about a spacetime. This may include local curvature, for instance around a star or black hole, gravitational radiation coming from a binary pulsar and even the large scale structure of the universe such as the rate of expansion. By performing local experiments one may attempt to extract this information. Fundamentally these experiments will be governed by quantum mechanics, hence the accuracy of the estimation will be fundamentally limited by the statistical nature of quantum theory. In this thesis we shall develop an equation which states just what accuracy one can ultimately achieve when attempting to measure the structure of spacetime. This equation will be shown to be a generalisation of known results for the accuracy to which one can ultimately measure position and momentum as well as time and energy. The result will be applied to a range of relativistic phenomena including acceleration in flat spacetime, the local curvature around a black hole, the amplitude of a gravitational wave and the expansion of the universe in a cosmological model. Following the use of quantum information theory to investigate gravity we shall look at how acceleration can effect quantum information. Firstly we shall see how quantum entanglement can be created and stored between two optical cavities when one is uniformly accelerating. This is in contrast to a number of results which predict that entanglement will be lost in the presence of acceleration. This loss of entanglement is predicted due to an as yet unobserved phenomena known as the Unruh effect. The Unruh effect states that an observer uniformly accelerating will see a thermal distribution of particles even if an inertial observer will see no particles at all. We will show how the use of optical cavities can prevent this effect from causing problems both for the storage and creation of entanglement. Finally we shall look at how a particular quantum detection scheme can be employed in the presence of acceleration. Our technique will emphasis the importance of locality, that is the localisation of physics in spacetime. We will also show how some commonly used approximations used to study the Unruh effect, can be avoided with our new formulation.
Keyword Quantum information
General relativity
Quantum field theory in curved spacetime
Quantum parameter estimation

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Created: Sun, 20 May 2012, 13:34:54 EST by Tony Downes on behalf of Library - Information Access Service