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  • 3 - Born’s Rule from the Symmetries of Entanglement

  • from Part I - Foundations
  • Wojciech Hubert Zurek, Los Alamos National Laboratory
  • Book:
    Decoherence and Quantum Darwinism
    Published online:
    06 March 2025
    Print publication:
    13 March 2025, pp 44-74

  • Summary

    Chapter 3 describes how quantum entanglement leads to probabilities based on a symmetry, but—in contrast to subjective equal likelihood based solely on ignorance—it is an objective symmetry of known quantum states. Entanglement-assisted invariance (or envariance for short) relies on quantum correlations: One can know the quantum state of the whole and use this to quantify the resulting ignorance of the states of parts. Thus, quantum probability is, in effect, an objective consequence of the Heisenberg-like indeterminacy between global and local observables. This derivation of Born’s rule is based on the consistent subset of quantum postulates. It justifies statistical interpretation of reduced density matrices, an indispensable tool of decoherence theory. Hence, it gives one the mandate to explore—in Part II of this book—the fundamental implications of decoherence and its consequences using reduced density matrices and other customary tools.