Quantum Theory From Five Reasonable Axioms. Hardy, L. 2001. cite arxiv:quant-ph/0101012Comment: 34 pages. Version 4: Improved proofs of K=N^r and D=D^T. Discussion of state update rule after measurement added. Various clarifications in proofs Version 2: Axiom 2 modified and corresponding corrections made to proof in Sec. 8.1. Typos and minor errors fixed
Paper abstract bibtex The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be derived from five very reasonable axioms. The first four of these are obviously consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead. This work provides some insight into the reasons quantum theory is the way it is. For example, it explains the need for complex numbers and where the trace formula comes from. We also gain insight into the relationship between quantum theory and classical probability theory.
@misc{hardy2001quantum,
abstract = {The usual formulation of quantum theory is based on rather obscure axioms
(employing complex Hilbert spaces, Hermitean operators, and the trace rule for
calculating probabilities). In this paper it is shown that quantum theory can
be derived from five very reasonable axioms. The first four of these are
obviously consistent with both quantum theory and classical probability theory.
Axiom 5 (which requires that there exists continuous reversible transformations
between pure states) rules out classical probability theory. If Axiom 5 (or
even just the word "continuous" from Axiom 5) is dropped then we obtain
classical probability theory instead. This work provides some insight into the
reasons quantum theory is the way it is. For example, it explains the need for
complex numbers and where the trace formula comes from. We also gain insight
into the relationship between quantum theory and classical probability theory.},
added-at = {2018-10-14T11:14:09.000+0200},
author = {Hardy, Lucien},
biburl = {https://www.bibsonomy.org/bibtex/20a590003ab9bafd8e3bf27ef2bf072ad/supremefacist},
description = {[quant-ph/0101012] Quantum Theory From Five Reasonable Axioms},
interhash = {f01e3ca1712c054dc07d7549b80f92bf},
intrahash = {0a590003ab9bafd8e3bf27ef2bf072ad},
keywords = {quantum_mechanics},
note = {cite arxiv:quant-ph/0101012Comment: 34 pages. Version 4: Improved proofs of K=N^r and D=D^T. Discussion of state update rule after measurement added. Various clarifications in proofs Version 2: Axiom 2 modified and corresponding corrections made to proof in Sec. 8.1. Typos and minor errors fixed},
timestamp = {2018-10-14T11:14:09.000+0200},
title = {Quantum Theory From Five Reasonable Axioms},
url = {http://arxiv.org/abs/quant-ph/0101012},
year = 2001
}
Downloads: 0
{"_id":"SJ8vDGeSoRwpKFJtE","bibbaseid":"hardy-quantumtheoryfromfivereasonableaxioms-2001","authorIDs":[],"author_short":["Hardy, L."],"bibdata":{"bibtype":"misc","type":"misc","abstract":"The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be derived from five very reasonable axioms. The first four of these are obviously consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word \"continuous\" from Axiom 5) is dropped then we obtain classical probability theory instead. This work provides some insight into the reasons quantum theory is the way it is. For example, it explains the need for complex numbers and where the trace formula comes from. We also gain insight into the relationship between quantum theory and classical probability theory.","added-at":"2018-10-14T11:14:09.000+0200","author":[{"propositions":[],"lastnames":["Hardy"],"firstnames":["Lucien"],"suffixes":[]}],"biburl":"https://www.bibsonomy.org/bibtex/20a590003ab9bafd8e3bf27ef2bf072ad/supremefacist","description":"[quant-ph/0101012] Quantum Theory From Five Reasonable Axioms","interhash":"f01e3ca1712c054dc07d7549b80f92bf","intrahash":"0a590003ab9bafd8e3bf27ef2bf072ad","keywords":"quantum_mechanics","note":"cite arxiv:quant-ph/0101012Comment: 34 pages. Version 4: Improved proofs of K=N^r and D=D^T. Discussion of state update rule after measurement added. Various clarifications in proofs Version 2: Axiom 2 modified and corresponding corrections made to proof in Sec. 8.1. Typos and minor errors fixed","timestamp":"2018-10-14T11:14:09.000+0200","title":"Quantum Theory From Five Reasonable Axioms","url":"http://arxiv.org/abs/quant-ph/0101012","year":"2001","bibtex":"@misc{hardy2001quantum,\n abstract = {The usual formulation of quantum theory is based on rather obscure axioms\r\n(employing complex Hilbert spaces, Hermitean operators, and the trace rule for\r\ncalculating probabilities). In this paper it is shown that quantum theory can\r\nbe derived from five very reasonable axioms. The first four of these are\r\nobviously consistent with both quantum theory and classical probability theory.\r\nAxiom 5 (which requires that there exists continuous reversible transformations\r\nbetween pure states) rules out classical probability theory. If Axiom 5 (or\r\neven just the word \"continuous\" from Axiom 5) is dropped then we obtain\r\nclassical probability theory instead. This work provides some insight into the\r\nreasons quantum theory is the way it is. For example, it explains the need for\r\ncomplex numbers and where the trace formula comes from. We also gain insight\r\ninto the relationship between quantum theory and classical probability theory.},\n added-at = {2018-10-14T11:14:09.000+0200},\n author = {Hardy, Lucien},\n biburl = {https://www.bibsonomy.org/bibtex/20a590003ab9bafd8e3bf27ef2bf072ad/supremefacist},\n description = {[quant-ph/0101012] Quantum Theory From Five Reasonable Axioms},\n interhash = {f01e3ca1712c054dc07d7549b80f92bf},\n intrahash = {0a590003ab9bafd8e3bf27ef2bf072ad},\n keywords = {quantum_mechanics},\n note = {cite arxiv:quant-ph/0101012Comment: 34 pages. Version 4: Improved proofs of K=N^r and D=D^T. Discussion of state update rule after measurement added. Various clarifications in proofs Version 2: Axiom 2 modified and corresponding corrections made to proof in Sec. 8.1. Typos and minor errors fixed},\n timestamp = {2018-10-14T11:14:09.000+0200},\n title = {Quantum Theory From Five Reasonable Axioms},\n url = {http://arxiv.org/abs/quant-ph/0101012},\n year = 2001\n}\n\n","author_short":["Hardy, L."],"key":"hardy2001quantum","id":"hardy2001quantum","bibbaseid":"hardy-quantumtheoryfromfivereasonableaxioms-2001","role":"author","urls":{"Paper":"http://arxiv.org/abs/quant-ph/0101012"},"keyword":["quantum_mechanics"],"metadata":{"authorlinks":{}},"downloads":0,"html":""},"bibtype":"misc","biburl":"http://www.bibsonomy.org/bib/author/Hardy?items=1000","creationDate":"2020-01-27T02:13:34.757Z","downloads":0,"keywords":["quantum_mechanics"],"search_terms":["quantum","theory","five","reasonable","axioms","hardy"],"title":"Quantum Theory From Five Reasonable Axioms","year":2001,"dataSources":["hEoKh4ygEAWbAZ5iy","rN3BH95XsZidWYd7J"]}