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**Tese de doutorado****Defendida**

# **Micro-to-macro and Macro-to-micro Quantum Mapping: a Coarse-graining Approach**

**Correia, Pedro Silva**

19/03/2021

[**Baixar PDF **5 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd78a/pdf) [**Contatar responsável**](mailto:denise@cbpf.br?subject=Micro-to-macro%20and%20Macro-to-micro%20Quantum%20Mapping%3A%20a%20Coarse-graining%20Approach)

## **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.

## **Dados da publicação**

<dl>

<dt>Autores</dt>
<dd>Correia, Pedro Silva</dd>

<dt>Tipo</dt>
<dd>Tese de doutorado</dd>

<dt>Status</dt>
<dd>Defendida</dd>

<dt>Data de publicação</dt>
<dd>19/03/2021</dd>

<dt>Instituição</dt>
<dd>CBPF</dd>

<dt>Data de defesa</dt>
<dd>19/03/2021</dd>

</dl>

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