# Most incompatible measurements for robust steering tests

## TL;DR

This paper investigates the limits of quantum state steerability under various measurement restrictions, proposing methods to evaluate measurement incompatibility and identifying measurement sets that are most incompatible for steering tests.

## Contribution

It introduces general bounds for noise robustness in quantum steering under different measurement scenarios and identifies measurement sets that are most incompatible for steering.

## Key findings

- Mutually unbiased bases and symmetric measurements are not optimal for steering isotropic states.
- Nonprojective POVMs do not outperform projective measurements in this context.
- Provided numerical evidence supporting the limitations of nonprojective POVMs.

## Abstract

We address the problem of characterizing the steerability of quantum states under restrictive measurement scenarios, i.e., the problem of determining whether a quantum state can demonstrate steering when subjected to $N$ measurements of $k$ outcomes. We consider the cases of either general positive operator-valued measures (POVMs) or specific kinds of measurements (e.g., projective or symmetric). We propose general methods to calculate lower and upper bounds for the white-noise robustness of a $d$-dimensional quantum state under different measurement scenarios that are also applicable to the study of the noise robustness of the incompatibility of sets of unknown qudit measurements. We show that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not optimal for steering isotropic states and provide candidates to the most incompatible sets of measurements in each case. Finally, we provide numerical evidence that nonprojective POVMs do not improve over projective ones for this task.