dorsal/arxiv
View SchemaA Bayesian Account of Quantum Histories
| Authors | Thomas Marlow |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509149 |
| URL | https://arxiv.org/abs/quant-ph/0509149 |
| DOI | 10.1016/j.aop.2005.09.006 |
| Journal | Annals of Physics 321 (2006) 1103--1125 |
Abstract
We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different approaches to formalising multi-time measurements in quantum theory. The standard approach consists of describing an ordered series of measurements in terms of history propositions with non-additive `probabilities'. The non-standard approach consists of defining multi-time measurements to consist of sets of exclusive and exhaustive history propositions and recovering the single-time exclusivity of results when discussing single-time history propositions. We analyse whether such history propositions can be consistent with Bayes' rule. We show that certain class of histories are given a natural Bayesian interpretation, namely the linearly positive histories originally introduced by Goldstein and Page. Thus we argue that this gives a certain amount of interpretational clarity to the non-standard approach. We also attempt a justification of our analysis using Cox's axioms of probability theory.
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"abstract": "We investigate whether quantum history theories can be consistent with\nBayesian reasoning and whether such an analysis helps clarify the\ninterpretation of such theories. First, we summarise and extend recent work\ncategorising two different approaches to formalising multi-time measurements in\nquantum theory. The standard approach consists of describing an ordered series\nof measurements in terms of history propositions with non-additive\n`probabilities\u0027. The non-standard approach consists of defining multi-time\nmeasurements to consist of sets of exclusive and exhaustive history\npropositions and recovering the single-time exclusivity of results when\ndiscussing single-time history propositions. We analyse whether such history\npropositions can be consistent with Bayes\u0027 rule. We show that certain class of\nhistories are given a natural Bayesian interpretation, namely the linearly\npositive histories originally introduced by Goldstein and Page. Thus we argue\nthat this gives a certain amount of interpretational clarity to the\nnon-standard approach. We also attempt a justification of our analysis using\nCox\u0027s axioms of probability theory.",
"arxiv_id": "quant-ph/0509149",
"authors": [
"Thomas Marlow"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2005.09.006",
"journal_ref": "Annals of Physics 321 (2006) 1103--1125",
"title": "A Bayesian Account of Quantum Histories",
"url": "https://arxiv.org/abs/quant-ph/0509149"
},
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