Resumo: If quantum mechanics is the fundamental theory in physics, at least in principle, it must assign states at every level of description of a system. Consequently, quantum mechanics must provide a two-way of describing nature. Firstly, the theory should connect a microscopic state to a macroscopic (effective) description of a system. Secondly, in an opposite direction, assuming access only to a macroscopic description of a system, quantum
mechanics must assign to it an ensemble of microscopic quantum states that abides by all macroscopic constraints. This thesis proposes to investigate both directions, which we named micro-to-macro mapping and macro-to-micro mapping. We first formalize a coarse-graining map that plays the role of a general micro-to-macro mapping. Such an approach aims to model general macroscopic descriptions of a quantum system, even when
there is an ambiguity in the split between system’s and environment’s degrees of freedom. As an application, we construct a coarse-graining map to model an imperfect detection of a well-isolated spin-system in an optical lattice scenario. We readily apply this coarsegraining to describe spin-entanglement dynamics in different ranges of resolution of the system. In the second part of the thesis, assuming that our macroscopic perception of nature is inherently coarse-grained, we construct a macro-to-micro operation called averaging
assignment map. This map assigns to a set of macroscopic coarse-grained observations a microscopic description which is the ensemble-average of all microscopic states that are compatible with that effective observations. As an application, we construct a nonlinear stochastic state dynamical map that emerges from underlying deterministic linearquantum evolution. As a by-product, we show how effective nonlinear dynamics can
be used to improve state discrimination.
|
