Parametrization of projector-based witnesses for bipartite systems

TL;DR

This paper introduces a new parametrization method for projector-based entanglement witnesses in bipartite systems, enabling effective detection of entanglement near pure states with simple operational procedures.

Contribution

It provides a general parametrization for orthonormal bases to construct entanglement witnesses, facilitating symbolic and numerical calculations for bipartite entanglement detection.

Findings

Method successfully detects entanglement near pure states

Applicable to atom-field systems like Jaynes-Cummings model

Witness detection correlates with negativity measures

Abstract

Entanglement witnesses are nonpositive Hermitian operators which can detect the presence of entanglement. In this paper, we provide a general parametrization for orthonormal basis of ${\mathbb C}^n$ and use it to construct projector-based witness operators for entanglement detection in the vicinity of pure bipartite states. Our method to parameterize entanglement witnesses is operationally simple and could be used for doing symbolic and numerical calculations. As an example we use the method for detecting entanglement between an atom and the single mode of quantized field, described by the Jaynes-Cummings model. We also compare the detection of witnesses with the negativity of the state, and show that in the vicinity of pure stats such constructed witnesses able to detect entanglement of the state.