Applications of the Stroboscopic Tomography to Selected 2-Level Decoherence Models

TL;DR

This paper explores how stroboscopic tomography can be applied to analyze the observability of 2-level quantum systems undergoing decoherence, focusing on optimal measurement strategies over time.

Contribution

It introduces a framework for applying stroboscopic tomography to decoherence models, identifying minimal measurement requirements for system observability.

Findings

Derived criteria for system observability under decoherence

Identified minimal number of observables and measurements needed

Provided insights into measurement strategies for quantum state reconstruction

Abstract

In the paper we discuss possible applications of the so-called stroboscopic tomography (stroboscopic observability) to selected decoherence models of 2-level quantum systems. The main assumption behind our reasoning claims that the time evolution of the analyzed system is given by a master equation of the form $\dot{\rho} = \mathbb{L} \rho$ and the macroscopic information about the system is provided by the mean values $m_i (t_j) = Tr(Q_i \rho(t_j))$ of certain observables $\{Q_i\}_{i=1} ^r $ measured at different time instants $\{t_j\}_{j=1}^p$. The goal of the stroboscopic tomography is to establish the optimal criteria for observability of a quantum system, i.e. minimal value of $r$ and $p$ as well as the properties of the observables $\{Q_i\}_{i=1} ^r $.