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Conference Paper: Operational axioms for diagonalizing states

TitleOperational axioms for diagonalizing states
Authors
Issue Date2015
Citation
The 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, UK., 13-17 July 2015. In EPTCS, 2015, v. 195, p. 96-115 How to Cite?
AbstractIn quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This feature is crucial for quantum statistical mechanics, as it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect that occurs with unit probability on some state. Using these axioms, we present a constructive method to decompose every given state into perfectly distinguishable pure states.
Persistent Identifierhttp://hdl.handle.net/10722/229702

 

DC FieldValueLanguage
dc.contributor.authorChiribella, G-
dc.contributor.authorScandolo, CM-
dc.date.accessioned2016-08-23T14:12:46Z-
dc.date.available2016-08-23T14:12:46Z-
dc.date.issued2015-
dc.identifier.citationThe 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, UK., 13-17 July 2015. In EPTCS, 2015, v. 195, p. 96-115-
dc.identifier.urihttp://hdl.handle.net/10722/229702-
dc.description.abstractIn quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This feature is crucial for quantum statistical mechanics, as it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect that occurs with unit probability on some state. Using these axioms, we present a constructive method to decompose every given state into perfectly distinguishable pure states.-
dc.languageeng-
dc.relation.ispartofElectronic Proceedings in Theoretical Computer Science (EPTCS)-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleOperational axioms for diagonalizing states-
dc.typeConference_Paper-
dc.identifier.emailChiribella, G: giulio@hku.hk-
dc.identifier.authorityChiribella, G=rp02035-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.4204/EPTCS.195.8-
dc.identifier.hkuros259991-
dc.identifier.volume195-
dc.identifier.spage96-
dc.identifier.epage115-
dc.customcontrol.immutablesml 160824-

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