Quantum violation of macrorealism under multi-outcome two-parameter generalised measurements

Abstract: Generalised dichotomic quantum measurements are fully characterised by two real parameters, dubbed as sharpness parameter and biasedness parameter. The trade-off between the degree of joint measurability, sharpness and biasedness of generalised measurements was known in the case of pairs of qubit observables. In the present work we generalise the notion of sharpness and biasedness measure of multi-outcome generalised measurements pertaining to multilevel systems. A trade-off between the amount of quantum mechanical (QM) violation of macrorealism (MR), sharpness and biasedness is established. Specifically we found that the minimum value of sharpness parameter, above which the QM violations of different necessary conditions of MR persist, decreases with increase in biasedness. We also analysed the effect of biasedness parameter on the magnitudes of QM violations of different necessary conditions of MR for multilevel spin systems.