Jordan Form and Quantum Tomography

TL;DR

This paper establishes a link between Jordan normal form in linear algebra and the stroboscopic approach to quantum tomography, providing a new way to analyze quantum state evolution.

Contribution

It introduces a method to compute the cyclicity index of quantum evolution generators using Jordan decomposition, connecting quantum tomography with linear algebra techniques.

Findings

Cyclicity index can be derived from Jordan form

Provides a linear algebra framework for quantum tomography

Bridges concepts between quantum physics and matrix theory

Abstract

In this brief article we indicate a connection between Jordan normal form of a square matrix and the stroboscopic approach to quantum tomography. We show that the index of cyclicy of a generator of evolution, which receives much attention in the stroboscopic tomography, can be defined and computed by referring to the Jordan decomposition of a square matrix. The result presented in this work shows a relation between terminology from quantum tomography and linear algebra.