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

Quantum Probability as an Application of Data Compression Principles