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**AI goalpost moving is not unreasonable (2)****Unital dynamics are mixedness increasing (1)****A checkable Lindbladian condition (2)****How to think about Quantum Mechanics—Part 1: Measurements are about bases (15)****Consistency conditions in consistent histories (3)****Lindblad operator trace is 1st-order contribution to Hamiltonian part of reduced dynamics (2)****Weingarten's branches from quantum complexity (1)**

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- Comments on Ollivier’s “Emergence of Objectivity for Quantum Many-Body Systems”November 27, 2023
- Compact precise definition of a transformer functionOctober 9, 2023
- Unital dynamics are mixedness increasingSeptember 27, 2023
- AI goalpost moving is not unreasonableJuly 21, 2023
- Notable reviews of arguments for AGI ruinApril 24, 2023
- Table of proposed macroscopic superpositionsApril 21, 2022
- GPT-3, PaLM, and look-up tablesApril 7, 2022
- Lindblad operator trace is 1st-order contribution to Hamiltonian part of reduced dynamicsMarch 14, 2022
- Weingarten’s branches from quantum complexityMarch 9, 2022
- How long-range coherence is encoded in the Weyl quasicharacteristic functionMay 18, 2021

- Comments on Ollivier’s “Emergence of Objectivity for Quantum Many-Body Systems”
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## Comments on Baldijao et al.’s GPT-generalized quantum Darwinism

This nice recent paper considers the “general probabilistic theory” operational framework, of which classical and quantum theories are special cases, and asks what sorts of theories admit quantum Darwinism-like dynamics. It is closely related to my interest in finding a satisfying theory of classical measurement.

Quantum Darwinism and the spreading of classical information in non-classical theoriesRoberto D. Baldijão, Marius Krumm, Andrew J. P. Garner, and Markus P. MüllerAfter the intro, the authors give self-contained background information on the two key prerequisites: quantum Darwinism and generalized probabilistic theories (GPTs). The former is an admirable brief summary of what are, to me, the core and extremely simple features of quantum Darwinism. This and the summary of GPT can be skipped by familiar readers, but I recommend reading definitions 1-4 in the latter part of the GPT subsection, plus the “Summary of Assumptions”.

The main results seems to be

reversiblequantum Darwinism process:The

reversiblequalifier is key here, as this statement excludes the possibility of Darwinism in classical models, whereas we of course know it’s possible to copy classical information in classical models with irreversible Markovian classical dynamics. ThusPhilosophically and aesthetically I like the idea of GPT as an operational framework for thinking about the foundations of quantum mechanics, although we should all be quite skeptical that GPTs besides quantum theory — either more or less expansive — will be found to describe any

fundamentalphysics (even though think it’s quite plausibly that quantum theory will eventually be superseded by something). This is because, among other things, GPTs treat space and time very different and especially because they take time asymmetry as fundamental rather than emergent or a consequence of initial conditions.The practical downside of GPTs is that there’s been a whole industry of papers exploring non-classical-or-quantum GPTs that don’t maintain contact with what could describe the real world; it’s too much fun to play with the math. This paper was a welcome exception, as it helps clarify which theories could lead to the appearance of classicality, at least insofar as the latter is identified with quantum Darwinsism.