Probabilistic theories with purification
Top Cited Papers
- 30 June 2010
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 81 (6)
- https://doi.org/10.1103/physreva.81.062348
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-Jamio\l{}kowski 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.Keywords
Other Versions
This publication has 43 references indexed in Scilit:
- Particle-Hole Asymmetry and Brightening of Solitons in a Strongly Repulsive Bose-Einstein CondensatePhysical Review Letters, 2009
- Information causality as a physical principleNature, 2009
- Generalized No-Broadcasting TheoremPhysical Review Letters, 2007
- Information processing in generalized probabilistic theoriesPhysical Review A, 2007
- From Bell’s Theorem to Secure Quantum Key DistributionPhysical Review Letters, 2006
- General properties of nonsignaling theoriesPhysical Review A, 2006
- Entanglement swapping for generalized nonlocal correlationsPhysical Review A, 2006
- Popescu-Rohrlich Correlations as a Unit of NonlocalityPhysical Review Letters, 2005
- No Signaling and Quantum Key DistributionPhysical Review Letters, 2005
- Quantum nonlocality as an axiomFoundations of Physics, 1994