Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor

TL;DR

This paper explores the detection of bound entanglement in three-qubit GHZ-diagonal states using linear and nonlinear entanglement witnesses implemented on an IBM quantum processor, highlighting the superior detection capability of nonlinear witnesses.

Contribution

It introduces a quantum circuit for generating GHZ-diagonal states and compares the effectiveness of linear versus nonlinear entanglement witnesses in experimental settings.

Findings

Nonlinear witnesses detect entanglement where linear ones fail.

Experimental validation on IBM quantum processor confirms theoretical predictions.

Proposed circuit efficiently generates GHZ-diagonal states for entanglement analysis.

Abstract

We investigate bound entanglement in three-qubit mixed states which are diagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these states is detected using entanglement witnesses and the analysis focuses on states exhibiting positive partial transpose (PPT). We then compare the detection capabilities of optimal linear and nonlinear entanglement witnesses. In theory, both linear and nonlinear witnesses produce non-negative values for separable states and negative values for some entangled GHZ diagonal states with PPT, indicating the presence of entanglement. Our experimental results reveal that in cases where linear entanglement witnesses fail to detect entanglement, nonlinear witnesses are consistently able to identify its presence. Optimal linear and nonlinear witnesses were generated on an IBM quantum computer and their performance was evaluated using two bound entangled states (Kay and Kye states) from the literature, and randomly generated entangled states in the GHZ diagonal form. Additionally, we propose a general quantum circuit for generating a three-qubit GHZ diagonal mixed state using a six-qubit pure state on the IBM quantum processor. We experimentally implemented the circuit to obtain expectation values for three-qubit mixed states and compute the corresponding entanglement witnesses.