Measurement incompatibility cannot be stochastically distilled

• URL: http://arxiv.org/abs/2308.02252v1
• Date: Fri, 4 Aug 2023 11:18:39 GMT
• Title: Measurement incompatibility cannot be stochastically distilled
• Authors: Huan-Yu Ku, Chung-Yun Hsieh, and Costantino Budroni
• Abstract summary: We show that the incompatibility of a set of measurements cannot be increased by subjecting them to a filter. We are able to solve the problem of the steerability obtained with respect to the most general local filters.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We show that the incompatibility of a set of measurements cannot be increased 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. Expanding these ideas to Einstein-Podolsky-Rosen steering experiments, we are able to solve the problem of the maximum steerability obtained with respect to the most general local filters in a way that allows for an explicit calculation of the filter operation. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps.

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