The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism. Here we utilize the concepts of identical and similar preparation procedures to show t
he conceptual differences and mutual interconnections between the statistical and the conventional interpretation of quantum formalism. Although the statistical understanding, and its final logical consequence, hidden variables theories (this connexion being explained in the text), have a great intuitive appeal due to its fewer ontological difficulties, both recent experimental results and some theoretical developments seem to support an epistemic alternative closer to the conventional one. Nevertheless, we must not rule out the possibility that new theorems or new explanatory principles may modify the reigning supremacy of this interpretation.
It is argued that the traditional realist methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof rests on th
e violation by quantum mechanics of the foundational principles of that methodology. An alternative methodology, in which the construction of sciences finishes at the level of human experience, as standard quantum theory strongly suggests, is then conjectured.
Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as $rho=(1-lambda)C_{
rho}+lambda E_{rho}$, where $C_{rho}$ is a separable matrix whose rank equals that of $rho$ and the rank of $E_{rho}$ is strictly lower than that of $rho$. With the simple choice $C_{rho}=M_{1}otimes M_{2}$ we have a necessary condition of separability in terms of $lambda$, which is also sufficient if the rank of $E_{rho}$ equals 1. We give a first extension of this result to detect genuine entanglement in multipartite states and show a natural connection between the multipartite separability problem and the classification of pure states under stochastic local operations and classical communication (SLOCC). We argue that this approach is not exhausted with the first simple choices included herein.
We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of knowledge could be
, what could be called its magic precisely resides in this violation.
