Probabilistic theories with purification

Giulio Chiribella, Giacomo Mauro D’Ariano, and Paolo Perinotti
Phys. Rev. A 81, 062348 – Published 30 June 2010

Abstract

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-Jamiołkowski 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.

  • Received 13 October 2009

DOI:https://doi.org/10.1103/PhysRevA.81.062348

©2010 American Physical Society

Authors & Affiliations

Giulio Chiribella*

  • Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Ontario, Ontario N2L 2Y5, Canada†

Giacomo Mauro D’Ariano and Paolo Perinotti§

  • QUIT Group, Dipartimento di Fisica “A. Volta” and INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy∥

  • *gchiribella@perimeterinstitute.ca
  • http://www.perimeterinstitute.ca
  • dariano@unipv.it
  • §paolo.perinotti@unipv.it
  • http://www.qubit.it

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Issue

Vol. 81, Iss. 6 — June 2010

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