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

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 me...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-02
Main Authors: Szymusiak, Anna, Słomczyński, Wojciech
Format: Article
Language:English
Subjects:
Probability theory
Quantum mechanics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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'.
ISSN:2331-8422