We show that the quantum advantages arising from incompatibility of a set of measurements cannot be enhanced by subjecting them to a filter, namely, by combining them with a device that post-selects the incoming states on a fixed outcome of a stochastic transformation. This result holds for several measures of incompatibility, such as those based on robustness and convex weight. As an application, we show that, for Einstein-Podolsky-Rosen steering, our no-go results determine the maximum steerability attainable under the most general local filters, together with an explicit expression for the optimal filter. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps.

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A theoretical quantum information paper proving that quantum advantages arising from measurement incompatibility cannot be enhanced by probabilistic filtering (post-selection via stochastic transformations). The no-go results hold for multiple incompatibility measures including robustness and convex weight. As an application, the results determine the maximum steerability achievable under general local filters for Einstein-Podolsky-Rosen steering, including an explicit optimal filter construction. The results also generalize to nonphysical (positive but not completely positive) linear maps.

No-go theorems on probabilistically enhancing measurement incompatibility’s advantages