Broadcasting of NPT Entanglement in Two Qutrit Systems

TL;DR

This paper investigates how much NPT entanglement can be broadcast in 3x3 quantum systems using approximate cloning, revealing insights into entanglement distribution and the existence of absolute PPT states.

Contribution

It analyzes the broadcasting range of NPT entanglement in 3x3 systems for specific state classes and identifies the presence of absolute PPT states using cloning strategies.

Findings

Range of broadcasting NPT entanglement for TPCS and IS

Existence of absolute PPT states in 3x3 systems

Broadcasting achieved through approximate cloning

Abstract

It is known that beyond $2 \otimes 2$ and $2 \otimes 3$ dimensional quantum systems, Peres-Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there can exist bound entangled states as well as free entangled states. All free/useful/distillable entanglement is a part of the class of NPT entangled states. In this article, we ask the question that given an NPT entangled state in $3 \otimes3$ dimensional system as a resource, how much entanglement can we broadcast so that resource still remains NPT. We have chosen $3 \otimes 3$ system as a first step to understand broadcasting of NPT states in higher dimensional systems. In particular, we find out the range of broadcasting of NPT entanglement for Two parameter Class of States (TPCS) and Isotropic States (IS). Interestingly, as a derivative of this process we are also able to locate the existence of absolute PPT states (ABPPT) in $3 \otimes 3$ dimensional system. Here we implement the strategy of broadcasting through approximate cloning operations.