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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 several characteristic indicators, namely entanglement of formation and concurrence, 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.

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We shortly review Bell-diagonal and Werner states of two quantum bits and their characterization, and carry out a detailed experimental study of their generation on the IBM Quantum Experience.To this end we propose new circuits and tomography. One circuit involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. For the first time the entire class of Bell-diagonal states is generated. A number of characteristic indicators, namely entanglement of formation, CHSH non-locality, steering and quantum discord, are evaluated over the full parameter space and compared with theory.