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Conference Paper: Operational axioms for diagonalizing states
Title  Operational axioms for diagonalizing states 

Authors  
Issue Date  2015 
Citation  The 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, UK., 1317 July 2015. In EPTCS, 2015, v. 195, p. 96115 How to Cite? 
Abstract  In 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 Identifier  http://hdl.handle.net/10722/229702 
DC Field  Value  Language 

dc.contributor.author  Chiribella, G   
dc.contributor.author  Scandolo, CM   
dc.date.accessioned  20160823T14:12:46Z   
dc.date.available  20160823T14:12:46Z   
dc.date.issued  2015   
dc.identifier.citation  The 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, UK., 1317 July 2015. In EPTCS, 2015, v. 195, p. 96115   
dc.identifier.uri  http://hdl.handle.net/10722/229702   
dc.description.abstract  In 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.language  eng   
dc.relation.ispartof  Electronic Proceedings in Theoretical Computer Science (EPTCS)   
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.title  Operational axioms for diagonalizing states   
dc.type  Conference_Paper   
dc.identifier.email  Chiribella, G: giulio@hku.hk   
dc.identifier.authority  Chiribella, G=rp02035   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.4204/EPTCS.195.8   
dc.identifier.hkuros  259991   
dc.identifier.volume  195   
dc.identifier.spage  96   
dc.identifier.epage  115   
dc.customcontrol.immutable  sml 160824   