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This research introduces analytical universal parent measurements that surpass current state-of-the-art bounds for quantifying measurement incompatibility in quantum systems. By formalizing these constructions within sum-of-squares optimisation, the authors provide a method to improve upon previous analytical values and certify high-dimensional steering in a device-independent manner. The work advances fundamental quantum theory by establishing universal bounds applicable to all measurements, offering a more efficient framework for resource quantification.
Most incompatible measurements and sum-of-squares optimisation
arXiv:2509.10381v3 Announce Type: replace Abstract: Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a long-standing problem. In this work, we exhibit analytical universal parent measurements giving access to bounds that beat the state of the art. In particular, we can show that, for relevant robustnesses, sets of anticommuting observables give rise to the most incompatible dichotomic measurements. We also formalise the construction of such universal parent measurements in the framework of sum-of-squares optimisation and obtain preliminary numerical results demonstrating the power of the method by improving on our own analytical values. All results find direct application for demonstrating genuine high-dimensional steering, that is, certifying the dimensionality of a quantum system in a one-sided device-independent manner.
Abstract:Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a long-standing problem. In this work, we exhibit analytical universal parent measurements giving access to bounds that beat the state of the art. In particular, we can show that, for relevant robustnesses, sets of anticommuting observables give rise to the most incompatible dichotomic measurements. We also formalise the construction of such universal parent measurements in the framework of sum-of-squares optimisation and obtain preliminary numerical results demonstrating the power of the method by improving on our own analytical values. All results find direct application for demonstrating genuine high-dimensional steering, that is, certifying the dimensionality of a quantum system in a one-sided device-independent manner.
arXiv:2509.10381 [quant-ph]
(or arXiv:2509.10381v3 [quant-ph] for this version)
New J. Phys. 28, 064509 (2026)
https://doi.org/10.1088/1367-2630/ae72ba DOI(s) linking to related resources
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