dorsal/arxiv
View SchemaDecision theory and information propagation in quantum physics
| Authors | Alan Forrester |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604133 |
| URL | https://arxiv.org/abs/quant-ph/0604133 |
| DOI | 10.1016/j.shpsb.2007.02.004 |
| Journal | Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, Vol, 38, No. 4, Dec 2007, 815-831 |
Abstract
In recent papers, Zurek has objected to the decision-theoretic approach of Deutsch and Wallace to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born Rule for its validity. Using the Heisenberg Picture and quantum Darwinism - the notion that classical information is quantum information that can proliferate in the environment pioneered by Olliver et al - I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.
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"abstract": "In recent papers, Zurek has objected to the decision-theoretic approach of\nDeutsch and Wallace to deriving the Born rule for quantum probabilities on the\ngrounds that it courts circularity. Deutsch and Wallace assume that the many\nworlds theory is true and that decoherence gives rise to a preferred basis.\nHowever, decoherence arguments use the reduced density matrix, which relies\nupon the partial trace and hence upon the Born Rule for its validity. Using the\nHeisenberg Picture and quantum Darwinism - the notion that classical\ninformation is quantum information that can proliferate in the environment\npioneered by Olliver et al - I show that measurement interactions between two\nsystems only create correlations between a specific set of commuting\nobservables of system 1 and a specific set of commuting observables of system\n2. This argument picks out a unique basis in which information flows in the\ncorrelations between those sets of commuting observables. I then derive the\nBorn rule for both pure and mixed states and answer some other criticisms of\nthe decision theoretic approach to quantum probability.",
"arxiv_id": "quant-ph/0604133",
"authors": [
"Alan Forrester"
],
"categories": [
"quant-ph",
"physics.hist-ph"
],
"doi": "10.1016/j.shpsb.2007.02.004",
"journal_ref": "Studies In History and Philosophy of Science Part B: Studies In\n History and Philosophy of Modern Physics, Vol, 38, No. 4, Dec 2007, 815-831",
"title": "Decision theory and information propagation in quantum physics",
"url": "https://arxiv.org/abs/quant-ph/0604133"
},
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