Emerging dynamics arising from coarse-grained quantum systems

Abstract

The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, an one-theory-fits-all would be highly impractical. To not get lost in unnecessary details, effective descriptions are mandatory. Here we analyze what are the dynamics that may emerge from a full quantum description when one does not have access to all the degrees of freedom of a system. More concretely, we describe the properties of the dynamics that arise from quantum mechanics if one has only access to a coarse grained description of the system. We obtain that the effective maps are not necessarily of Kraus form, due to correlations between accessible and non-accessible degrees of freedom, and that the distance between two effective states may increase under the action of the effective map. We expect our framework to be useful for addressing questions such as the thermalization of closed quantum systems, as well as the description of measurements in quantum mechanics.

Coarse Graining of Partitioned Cellular Automata

“…Therefore, rather than extend the method showed in [2] to the QCA, a natural choice is picking up the prescription introduced here and extend it to its quantum version. In quantum theory this tool can be useful, for instance, to study the transition from the quantum to the classical world [25,26].…”

Quantum state reduction: Generalized bipartitions from algebras of observables

“…Kofler and Brukner [27] considered the emergence of classical physics from the coarse-graining inherent in measurements which can be performed with only finite precision. Duarte et al [28] have constructed a state-reduction map for a blurred and saturated detector and analyzed the reduced dynamics.…”

Decay of quantumness in a measurement process: Action of a coarse-graining channel

“…The approach devised in [9,10], however, is not dynamical, in the sense that it applies a coarse graining procedure directly on the measurement outcomes. Inspired by such results, in [11] the authors developed a framework that applies a coarse graining procedure directly on the manybody system. In this way they can obtain both the effective description of the system and its effective dynamics.…”