Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
arxiv(2024)
Abstract
In a bipartite Bell scenario involving two local measurements per party and
two outcome per measurement, the measurement incompatibility in one wing is
both necessary and sufficient to reveal the nonlocality. However, such a
one-to-one correspondence fails when one of the observers performs more than
two measurements. In such a scenario, the measurement incompatibility is
necessary but not sufficient to reveal the nonlocality. In this work, within
the formalism of general probabilistic theory (GPT), we demonstrate that unlike
the nonlocality, the incompatibility of N arbitrary measurements in one wing is
both necessary and sufficient for revealing the generalised contextuality for
the sub-system in the other wing. Further, we formulate a novel form of
inequality for any GPT that are necessary for N-wise compatibility of N
arbitrary observables. Moreover, we argue that any theory that violates the
proposed inequality possess a degree of incompatibility that can be quantified
through the amount of violation. Finally, we claim that it is the generalised
contextuality that provides a restriction to the allowed degree of measurement
incompatibility of any viable theory of nature and thereby super-select the the
quantum theory.
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