Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

TL;DR

This paper introduces a new indecomposable positive map for two-qutrit systems that can generate and detect bound entangled states, advancing the methods for identifying complex quantum entanglement.

Contribution

It proposes a novel indecomposable positive map and a corresponding witness operator, along with a physical approximation to detect bound entanglement in higher-dimensional systems.

Findings

Generated a class of PPT states using the new map

Constructed a weakly optimal, locally implementable witness operator

Discovered a PPT entangled state undetectable by existing criteria

Abstract

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPT entangled state which is not detectable by certain other well-known entanglement detection criteria.