Operational axioms for diagonalizing states

EPTCS 195:96-115 (2015)

Authors
Carlo Maria Scandolo
University of Oxford
Abstract
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where 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 occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations.
Keywords Foundations of quantum thermodynamics  Foundations of quantum theory
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics.Howard Barnum - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):343-379.
Quantum Theory is an Information Theory.Giacomo M. D’Ariano & Paolo Perinotti - 2016 - Foundations of Physics 46 (3):269-281.
Random Quantum States.William K. Wootters - 1990 - Foundations of Physics 20 (11):1365-1378.
Probability Theories in General and Quantum Theory in Particular.L. Hardy - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):381-393.
Entropy in Operational Statistics and Quantum Logic.Carl A. Hein - 1979 - Foundations of Physics 9 (9-10):751-786.
Quantum States as Objective Informational Bridges.Richard Healey - 2017 - Foundations of Physics 47 (2):161-173.

Analytics

Added to PP index
2016-01-30

Total views
129 ( #61,490 of 2,273,206 )

Recent downloads (6 months)
50 ( #16,771 of 2,273,206 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature