Author ORCID Identifier
0009-0002-0227-8658
Date of Award
8-31-2026
Document Type
Open Access Thesis
Degree Name
Master of Science (MS)
Department
Physics, Applied
First Advisor
Christopher Fuchs
Abstract
Experimental violations of Bell's inequality demonstrate quantum theory's incompatibility with a local hidden-variable formulation. Simply put, either 1) measurements performed at one point in space may instantaneously influence far away systems ("spooky action at a distance") or 2) measurement outcomes are not the result of pre-existing properties. The act of measurement takes part in the very creation of the outcomes. If we reject condition 1 as a valid assumption, how can we interpret the significance of condition 2 i.e. no local parameters? In QBism, condition 2 arises from something deeper: that the Born rule expresses a nonclassical condition for connecting probabilities between disparate experiments.
Equipped with minimally informationally-complete positive operator valued measures (MICs), it is possible to reformulate the Born rule purely in terms of probabilities without invoking quantum states or measurement operators. This formulation makes it possible to compare the Born rule to the classical Law of Total Probability (LTP). Previous authors have demonstrated that the form of the Born rule obtained from a symmetric informationally-complete measure (SIC) minimizes its deviation from the LTP with respect to unitarily invariant distance measures. In this work, we demonstrate that this result is not limited to distance measures with the unitary invariance property. For entrywise p-norms p > 1, SICs minimize the deviation of the Born rule from the LTP as well.
Recommended Citation
Monaghan, Austin, "Symmetric Informationally Complete Positive Operator Valued Measures Minimize p-norm Difference Between Quantum and Classical Probability Rules" (2026). Graduate Masters Theses. 972.
https://scholarworks.umb.edu/masters_theses/972
Comments
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