Abstract
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born’s rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as “unitary quantum mechanics”, and the assumption that ensembles on finite-dimensional Hilbert spaces are characterized by finitely many parameters. This is achieved by taking an operational approach to physical theories, and using the fact that the manner in which a physical system is partitioned into subsystems is a subjective choice of the observer, and hence should not affect the predictions of the theory. In contrast to other approaches, our result does not assume that measurements are related to operators or bases, it does not rely on the universality of quantum mechanics, and it is independent of the interpretation of probability.
Highlights
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory
Deciding to describe a tripartite system A·B·C as either the bipartite system AB·C or as A·BC must not modify the outcome probabilities. Using these constraints we characterize all possible alternatives to the mathematical structure of quantum measurements and the Born rule, and we prove that there is no such alternative to the standard measurement postulates
Before presenting the main result we prepare the stage appropriately. This involves reviewing some of the postulates of quantum mechanics (QM), reconstructing the structure of mixed states from them, and introducing a general characterization of measurements that is independent of their mathematical structure
Summary
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. We show that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born’s rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as “unitary quantum mechanics”, and the assumption that ensembles on finite-dimensional Hilbert spaces are characterized by finitely many parameters This is achieved by taking an operational approach to physical theories, and using the fact that the manner in which a physical system is partitioned into subsystems is a subjective choice of the observer, and should not affect the predictions of the theory. A further interesting consequence of this theorem is that the post-measurement state-update rule must necessarily be that of QM
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