Quantum Physics

The standard approach to quantum nonlocality (Bell's Theorem) relies on the assumption of the existence of "free will". I will explain how to get rid of this mysterious assumption in favor of the independence of sources. From this new point of view, Bell's Theorem becomes a statement about Bayesian networks. Besides allowing a more intuitive formulation of the standard result, our formalism also provides new network topologies giving rise to new kinds of nonlocality. Some of these relate to results by Steudel and Ay on the statistical inference of causal relations. Witnessing quantum nonlocality in new network topologies is a challenge which I will pose as an open problem.

We present a quantization method based on theEhrenfest theorem embedded in an extended algebraic structure capableof consistently describing hybrid quantum-classical systems, where thestandard quantum and classical mechanics are two limiting cases. TheWigner phase space formulation and the Schordinger equation are foundto be two alternative representations of the quantum case while theKoopman-von Neumann equation is the corresponding classicalcounterpart. Moreover, the developed quantization procedure isgeneralized to describe open systems, quantum/classical field theoriesand relativistic mechanics where new dynamical equations appear,shedding new light on important practical problems such asunderstanding of the quantum/classical transition and modeling ofmesoscopic systems.

Related references: arXiv:1105.4014, arXiv:1112.3679, arXiv:1107.5139

Categorical quantum mechanics (CQM) uses symmetric monoidal categories to formalize quantum theory, in order to extract the key structures that yield protocols such as teleportation in an abstract way. This formalism admits a purely graphical calculus, but the causal structure of these diagrams, and the formalism in general, is unclear. We begin by considering the signaling abilities of probabilistic devices with inputs and outputs and we show how a non-signaling device can become a perfect signaling device under time-reversal. This conflicts with the causal structure of relativity, and suggests that an `asymmetry' is needed when formalizing causality in CQM. We then show how a fixed causal structure within CQM corresponds to topological connectedness in the graphical language, and that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of a global state forces the monoidal product to be only partially defined, which in turn results in a covariance theorem. These structural results lead to a mathematical entity which we call a `causal category'.