A portrait of quantum mechanics as a theory of information processing
Giulio Chiribella ( Perimeter Institute for Theoretical Physics )

16:30 18th January 2011 ( week 1, Hilary Term 2011 )Lecture Theatre B
After more than eighty years since its rigorous mathematical formulation, quantum theory is still mysterious. Its usual textbook
presentations are merely descriptions of an abstract mathematical formalism, where``states are described by unit vectors in
a Hilbert space" and ``observables are described by selfadjoint operators". However, this approach leaves aside the question
about the underlying physical principles of the theory. For this reason, quantum theory is still far from providing a picture
of the physical world capable to compete with the simple picture that we inherited from classical physics. In this talk I
will explore the general idea that the new paradigm of physics could be that of information processing, and, specifically,
I will present a new result showing that the mathematics
of quantum theory can be completely reconstructed from a set of principles about information processing. The crucial feature
of these principles is that they are not of mathematical nature like the usual axioms in the Hilbert space formulation. Instead,
they can be formulated in a language that only refers to operational notions, like the notion of probabilistic mixture or
the notion or reversible transformation. The key principle in our reconstruction of quantum theory is the "purification principle",
stating that every mixed state of a system A can be obtained as the marginal state of some pure state of a joint system AB.
In other words, the principle requires that the ignorance about a part be always compatible with the maximal knowledge of
a whole. This statement reflects the original views by
Schroedinger on entanglement, and introduces in our basic theory of information processing all genuine quantum features, like
entanglement, the nocloning theorem, and the possibility of state teleportation.