Discretization of the density matrix as a nonlinear positive map and entanglement

TL;DR

This paper introduces a nonlinear positive map via density matrix discretization for continuous variable systems, enabling entanglement measurement through various criteria and analyzing the impact of discretization on system information.

Contribution

It presents a novel discretization method for density matrices as a nonlinear positive map and applies it to entanglement quantification in continuous variable systems.

Findings

Discretization effectively calculates entanglement measures.

Results agree with analytical solutions for two-mode squeezed states.

Discretization causes some information loss but remains useful.

Abstract

The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis entropy, von Neumann entropy and linear entropy and the logarithmic negativity. As an example, we study the dynamics of entanglement for the two-mode squeezed vacuum state in the parametric amplifier and show good agreement with the analytic results. The loss of information on the system state due to the discretization of the density matrix is also addressed.