Can QBism exist without Q? Morphophoric measurements in generalised probabilistic theories

• URL: http://arxiv.org/abs/2302.04957v1
• Date: Thu, 9 Feb 2023 22:21:17 GMT
• Title: Can QBism exist without Q? Morphophoric measurements in generalised probabilistic theories
• Authors: Anna Szymusiak, Wojciech S{\l}omczy\'nski
• Abstract summary: We show that the theory built on morphophoric measurements retains the chief features of the QBism approach to the basis of quantum mechanics. In particular, we demonstrate how to extend the primal equation (Urgleichung') of QBism, designed for SIC-POVMs, to the morphophoric case of GPTs.
• Score: 0.7614628596146599
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map transforming states into distributions of the measurement results is a similarity. In the quantum case, morphophoric measurements generalise the notion of a 2-design POVM, thus in particular that of a SIC-POVM. We show that the theory built on this class of measurements retains the chief features of the QBism approach to the basis of quantum mechanics. In particular, we demonstrate how to extend the primal equation (`Urgleichung') of QBism, designed for SIC-POVMs, to the morphophoric case of GPTs. In the latter setting, the equation takes a different, albeit more symmetric, form, but all the quantities that appear in it can be interpreted in probabilistic and operational terms, as in the original `Urgleichung'.

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