Bell Diagonal and Werner state generation: entanglement, non-locality, steering and discord on the IBM quantum computer

TL;DR

This paper presents the first correct quantum circuits for generating Bell-diagonal states on IBM quantum computers, enabling comprehensive experimental analysis of their quantum correlations including entanglement, non-locality, steering, and discord.

Contribution

It introduces novel, specialized quantum circuits for Bell-diagonal states and provides the first experimental characterization of their quantum correlations across the full parameter space.

Findings

Bell-diagonal states generated on IBM quantum computers match theoretical predictions.

Quantum discord is always less than or equal to the asymmetric relative entropy of discord for these states.

For all Bell-diagonal states, quantum discord and asymmetric relative entropy of discord are equal.

Abstract

We propose the first correct special-purpose quantum circuits for preparation of Bell-diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell-diagonal states is generated, and a number of characteristic indicators, namely entanglement of formation, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work we also find a remarkable general inequality between "quantum discord" and "asymmetric relative entropy of discord": the former never exceeds the latter. We also prove that for all BDS the two coincide.