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Probabilistic Theories with Purification

Chiribella, Giulio and D'Ariano, Giacomo Mauro and Perinotti, Paolo (2010) Probabilistic Theories with Purification. In: UNSPECIFIED.


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We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, namely that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows one to prove most of the basic features of quantum mechanics, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

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Item Type: Conference or Workshop Item (UNSPECIFIED)
Chiribella, Giulio
D'Ariano, Giacomo Mauro
Perinotti, Paolo
Keywords: axiomatics of quantum theory, conceptual foundations of quantum information processing, operational-probabilistic theories, causal theories, local tomography, reversible evolution, states of maximal knowledge, Stinespring's theorem, Ozawa's theorem, Naimark's theorem, teleportation, no-cloning theorem, error correction, bit commitment
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Giulio Chiribella
Date Deposited: 02 Jul 2010
Last Modified: 07 Oct 2010 15:19
Item ID: 5452
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: July 2010

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