Memories of the future. Predictable and unpredictable information in fractional flipping a biased coin

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Abstract

Some uncertainty about flipping a biased coin can be resolved from the sequence of coin sides shown already. We report the exact amounts of predictable and unpredictable information in flipping a biased coin. Fractional coin flipping does not reflect any physical process, being defined as a binomial power series of the transition matrix for “integer” flipping. Due to strong coupling between the tossing outcomes at different times, the side repeating probabilities assumed to be independent for “integer” flipping get entangled with one another for fractional flipping. The predictable and unpredictable information components vary smoothly with the fractional order parameter. The destructive interference between two incompatible hypotheses about the flipping outcome culminates in a fair coin, which stays fair also for fractional flipping.

Original languageEnglish
Article number807
JournalEntropy
Volume21
Issue number8
DOIs
StatePublished - Aug 2019

Keywords

  • Destructive interference of information
  • Fractional flipping a biased coin
  • Probability entanglement

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