Operational axioms for diagonalizing states

EPTCS 195:96-115 (2015)
Download Edit this record How to cite View on PhilPapers
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.
PhilPapers/Archive ID
CHIOAF-4
Revision history
Archival date: 2016-01-30
View upload history
References found in this work BETA
Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories.Barnum, Howard; Gaebler, Carl Philipp & Wilce, Alexander
Quantum Computation and Quantum Information.Nielson, M. A. & Chuang, I. L.

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2016-01-30

Total views
122 ( #24,759 of 43,699 )

Recent downloads (6 months)
49 ( #14,906 of 43,699 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.