Resumo: Motivated by the recent assignment of the 2022 Nobel prize to Aspect, Clauser and Zeilinger, I present a course on fundaments of quantum mechanics. The aim of the course is to revisit fundamental aspects (and possible generalizations) of quantum mechanics with stress on what can be simulated (up to which point) and what cannot be simulated by classical physics. I introduce the notion of discretized qubit to make a bridge between quantum physics and information and classical physics and information described by ordinary bits. Manipulation of spin-states will be revisited in the framework of discretized qubits: quantum measurement and the collapse of the wave function, superposition, entanglement, quantum Zeno effect, EPR gedanken experiments. I illustrate the infamous dead-live cat superposed state by pointing out a mechanism which can allow this state not to be observable. I will illustrate that EPR measurements which do not violate Bell’s inequalities can be reproduced by protocols with Alice and Bob who (before separating to move to far away laboratories) locally share hidden variables. In the EPR measurements which violate the Bell’s inequality a new feature appears. Different ways to detect it make use of negative probabilities, spooky action at a distance, and superdeterminism. In the last part of the course I will describe the notion of parastatistics and the detectability of multiparticle states which go beyond ordinary bosons and fermions. The first part of the course is based on a talk, where I introduced the notion of discretized qubits, given in Lavras for the “Minicurso de física quântica na cidade dos ipês e das escolas” realized on May 2022. The video of the talk is available in Youtube:
The second part of the course on parastatistics is based on my 2020 course at the XIII Escola do CBPF, complemented with the new results presented in my talk on Oct. 19, 2022 at the XII Workshop de Física Teórica at CBPF.
