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

## TL;DR

This paper explores how multi-outcome generalized measurements affect quantum violations of macrorealism in multilevel systems, revealing a trade-off between measurement parameters and quantum violations.

## Contribution

It generalizes the measures of sharpness and biasedness for multi-outcome measurements in multilevel systems and establishes their impact on quantum violations of macrorealism.

## Key findings

- Minimum sharpness decreases with increased biasedness for persistent QM violations.
- Biasedness influences the magnitude of QM violations in multilevel spin systems.
- Trade-off identified between measurement parameters and macrorealism violations.

## 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.