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Fundamental quantum mechanics, a didactic proposal. De estas nociones base se presenta su formalismo para sistemas de dos niveles. Fundamental quantum mechanics FQM is a commented presentation of fundamental experiments and concepts of quantum mechanics, the physical theory of the quantum phenomena domain: superposition principle and quantum entanglement become the cornestone of the theoretical foundation of the quantum description. The formalism of these basic notions, for two-level systems, is presented. Also, the quantum measurement problem is stated through the discussion of the ideas of probability, evolution dynamics and measurement. Finally, this theoretical construction is contextualized in emblematic experiments of the quantum domain: the two slit experiment, the Stern-Gerlach experiment and the Mach-Zehnder interferometer, and in technological applications, such as quantum teleportation and quantum cryptography.

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Mitchell and Valerio Pruneri, played a critical role in the historic experiment was published online today in Nature by the group of Ronald Hanson at TU Delft. In a mathematical sense, they lose their identities. When measured, the Delft electrons did indeed appear individually random while agreeing very well. So well, in fact, that they cannot have had pre-existing orientations, as realism claims.

This behaviour is only possible if the electrons communicate with each other, something that is very surprising for electrons trapped in different crystals.

But if they communicated, they must have done so faster than the speed of light. This amazing experiment called for extremely fast, unpredictable decisions about how to measure the electron orientations. The team constituted Carlos Abellan, Waldimar Amaya, Valerio Pruneri and Morgan Mitchell hold the record for the fastest quantum random number generators.

This produced one extremely pure random bit for each measurement made in the Delft experiment. The bits were produced in about ns, the time it takes light to travel just 30 meters, not nearly enough time for the electrons to communicate.

Never before has an experiment required such good random numbers in such a short time. For the ICFO team, the participation in the Delft experiment was more than a chance to contribute to fundamental physics. The laws that govern the Universe may indeed be a throw of the dice.

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Quantum entanglement is a physical phenomenon that occurs when a pair or group of particles is generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics : entanglement is a primary feature of quantum mechanics lacking in classical mechanics. Measurements of physical properties such as position , momentum , spin , and polarization performed on entangled particles are found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a property of a particle results in an irreversible wave function collapse of that particle and will change the original quantum state. In the case of entangled particles, such a measurement will affect the entangled system as a whole.

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