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Dynamics of a quantum reference frame

Poulin, David and Yard, Jon (2007) Dynamics of a quantum reference frame. New Journal of Physics, 9 (5). p. 156. ISSN 1367-2630. doi:10.1088/1367-2630/9/5/156.

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We analyse a quantum mechanical gyroscope which is modelled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyse the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in a time which scales linearly with the size of the reference. This contrasts with a recent conclusion of Bartlett et al that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles.

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Additional Information:Copyright © 2007 Deutsche Physikalische Gesellschaft & Institute of Physics Received 5 April 2007; Published 29 May 2007 We thank Stephen Bartlett and Peter Turner for comments on an earlier version of this manuscript, and Florian Girelli and Wojciech Zurek for useful conversations. This work was supported in part by the National Science Foundation under grant no. PHY-0456720. DP also receives financial support from the Gordon and Betty Moore Foundation through Caltech’s Centre for the Physics of Information and from the Natural Sciences and Engineering Research Council of Canada.
Issue or Number:5
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8071
Deposited By: Archive Administrator
Deposited On:23 Jul 2007
Last Modified:08 Nov 2021 20:47

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