Probabilistic theories with purification

By Giulio Chiribella, Giacomo Mauro D'Ariano, Paolo Perinotti. 2009

464 citations recorded by the source corpus.

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, that is, to the fact 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 theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d2aa4ecfe8f12c3e6dbe4442fb9bc4f37f8b6667

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

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Citations in the corpus

A derivation of quantum theory from physical requirements (2010, background): “The search for alternative axiomatizations of QT is an old topic that goes back to Birkhoff and von Neumann [8], and has been approached in many different ways: extending propositional logic [7, 8], using operational primitives [3–6], [9], searching for informationtheoretic principles [5, 6, 10, 11]”
Reformulating and Reconstructing Quantum Theory (2011, methodology): “First, Chiribella, D’Ariano, and Perinotti [14] showed that the success probability for probabilistic teleportation is bounded by the inverse of the number of probabilities required to specify a state (see Lemma 22 in [14]).”
Higher-order interference and single-system postulates characterizing quantum theory (2014, background): “Thus we are not making the assumption sometimes called the ‘no-restriction hypothesis’ [41, 50, 63] or ‘local saturation’ [64], nor the equivalent dual requirement (discussed, e.”
Theory-independent limits on correlations from generalized Bayesian networks (2014, methodology): “CDP use a graphical notation that builds upon that of Abramsky and Coecke [1].”