dorsal/arxiv
View SchemaDynamics of a Quantum Reference Frame
| Authors | David Poulin, Jon Yard |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612126 |
| URL | https://arxiv.org/abs/quant-ph/0612126 |
| DOI | 10.1088/1367-2630/9/5/156 |
| Journal | New J. Phys 9, 156 (2007) |
Abstract
We analyze a quantum mechanical gyroscope which is modeled 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 analyze 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 time which scales linearly with the size of the reference. This contrasts 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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"abstract": "We analyze a quantum mechanical gyroscope which is modeled as a large spin\nand used as a reference against which to measure the angular momenta of\nspin-1/2 particles. These measurements induce a back-action on the reference\nwhich is the central focus of our study. We begin by deriving explicit\nexpressions for the quantum channel representing the back-action. Then, we\nanalyze the dynamics incurred by the reference when it is used to sequentially\nmeasure particles drawn from a fixed ensemble. We prove that the reference\nthermalizes with the measured particles and find that generically, the thermal\nstate is reached in time which scales linearly with the size of the reference.\nThis contrasts a recent conclusion of Bartlett et al. that this takes a\nquadratic amount of time when the particles are completely unpolarized. We now\nunderstand their result in terms of a simple physical principle based on\nsymmetries and conservation laws. Finally, we initiate the study of the\nnon-equilibrium dynamics of the reference. Here we find that a reference in a\ncoherent state will essentially remain in one when measuring polarized\nparticles, while rotating itself to ultimately align with the polarization of\nthe particles.",
"arxiv_id": "quant-ph/0612126",
"authors": [
"David Poulin",
"Jon Yard"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/9/5/156",
"journal_ref": "New J. Phys 9, 156 (2007)",
"title": "Dynamics of a Quantum Reference Frame",
"url": "https://arxiv.org/abs/quant-ph/0612126"
},
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