Over the past decades there has been an intense work aiming at the reconstruction of quantum theory from principles that can be formulated without the mathematical framework of Hilbert spaces and operator algebras. The motivation was that these principles could provide a new angle to understand into the counterintuitive quantum laws, that they could reveal connections between different quantum features, and that they could provide guidance for constructing new quantum algorithms and for extending quantum theory to new physical scenarios.
In this talk I will discuss on one such principle, called the Purification Principle. Informally, the idea of the Purification Principle is that it is always possible to combine the incomplete information gathered by an observer with a maximally informative picture of the physical world. This idea resonates with Schrödinger’s famous quote that “[in quantum theory] the best possible knowledge of a whole does not necessarily imply the best possible knowledge of its parts”, a property that he called “not one, but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.”
References for this talk:
GC, GM D’Ariano, and P Perinotti, Probabilistic Theories with Purification, Phys. Rev. A 81, 062348 (2010)
GC, GM D’Ariano, and P Perinotti, Informational Derivation of Quantum Theory, Phys. Rev. A 84, 012311 (2011)
GM D’Ariano, GC, and P Perinotti, Quantum Theory From First Principles, Cambridge University Press (2017).