Teleportation criteria based on maximum eigenvalue of the shared $d\otimes d$ dimenional mixed state: Beyond Singlet Fraction

TL;DR

This paper introduces a new teleportation criterion for $d\otimes d$ entangled states based on the maximum eigenvalue, offering an experimentally accessible method beyond the traditional singlet fraction approach.

Contribution

The paper presents a novel eigenvalue-based criterion for detecting NPT entangled states useful for teleportation, simplifying experimental detection.

Findings

Criterion successfully detects NPT entangled states in qubit-qubit systems

Criterion extends to qutrit-qutrit systems

Easier experimental implementation than full state tomography

Abstract

We derive a criteria for the detection of $d\otimes d$ dimensional negative partial transpose (NPT) entangled state useful for teleportation. The newly derived criteria are based on the maximum eigenvalue of the NPT entangled state, which is easier to determine experimentally than to completely reconstruct the state via tomography. We then illustrate our criteria by considering a class of qubit-qubit system and qutrit-qutrit system.