A general dichotomization procedure to provide qudits entanglement criteria

TL;DR

This paper introduces a general method to derive entanglement criteria for qudits by mapping them to qubits, enabling the use of established qubit entanglement tests and extending variance-based witnesses to higher dimensions.

Contribution

The authors develop a universal mapping from qudits to qubits that preserves separability and rotational invariance, allowing existing qubit criteria to be applied to higher-dimensional systems.

Findings

Successfully detects entangled states in qudits using the proposed mapping.

Generalizes variance-based entanglement witnesses from qubits to qudits.

Demonstrates the effectiveness of the method with specific examples.

Abstract

We present a general strategy to derive entanglement criteria which consists in performing a mapping from qudits to qubits that preserves the separability of the parties and SU(2) rotational invariance. Consequently, it is possible to apply the well known positive partial transpose criterion to reveal the existence of quantum correlations between qudits. We discuss some examples of entangled states that are detected using the proposed strategy. Finally, we demonstrate, using our scheme, how some variance-based entanglement witnesses can be generalized from qubits to higher dimensional spin systems.