Allan F. Randall | Searcharxiv

arXiv2018

Objective and Subjective Solomonoff Probabilities in Quantum Mechanics

Algorithmic probability has shown some promise in dealing with the probability problem in the Everett interpretation, since it provides an objective, single-case probability measure. Many find the Everettian cosmology to be overly extravagant, however, and algorithmic probability has also provided improved models of subjective probability and Bayesian reasoning. I attempt here to generalize algorithmic Everettianism to more Bayesian and subjectivist interpretations. I present a general framework for applying generative probability, of which algorithmic probability can be considered a special case. I apply this framework to two commonly vexing thought experiments that have immediate application to quantum probability: the Sleeping Beauty and Replicator experiments.

quant-ph↗

arXiv2016

Quantum Probability as an Application of Data Compression Principles

Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be norm-squared (due to the Gleason-Busch Theorem) this fact conflicts with various popular, non-wavefunction-based phenomenological measures - such as observer, outcome or world counting - that are frequently demanded of Everettians. These alternatives conflict, however, with the wavefunction realism upon which Everett's approach rests, which seems to call for an objective, basis-independent measure based only on wavefunction amplitudes. The ability of quantum probabilities to destructively interfere with each other, however, makes it difficult to see how probabilities can be derived solely from amplitudes in an intuitively appealing way. I argue that the use of algorithmic probability can solve this problem, since the objective, single-case probability measure that wavefunction realism demands is exactly what algorithmic information theory was designed to provide. The result is an intuitive account of complex-valued amplitudes, as coefficients in an optimal lossy data compression, such that changes in algorithmic information content (entropy deltas) are associated with phenomenal transitions.

cs.IT↗