Singularity of dynamical maps

TL;DR

This paper introduces a method to identify and quantify singular points in quantum dynamical maps where the usual composition law fails, with applications demonstrated on specific examples and an extension to high-dimensional systems.

Contribution

It presents a novel approach to detect and measure singularities in quantum dynamical maps, extending the analysis to high-dimensional systems.

Findings

Method successfully identifies singular points in dynamical maps.

Calculated measures quantify the degree of singularity.

Extended approach applicable to high-dimensional quantum systems.

Abstract

For a dynamical map $\Lambda(t,0)$, which sends a state $\rho(0)$ of quantum open system to a state $\rho(t)=\Lambda(t,0)\rho(0)$, the decomposition law $\Lambda(t,0)=\Lambda(t,t_c)\Lambda(t_c,0)$ may break down at a specific time $t_c$. In this paper, we present a method to find the singular points $t_c$ and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, the measure of singularity for these singular points is calculated and discussed. An extension to high-dimensional system is presented.