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 language | English |
|---|---|
| Pages (from-to) | 12 |
| Journal | Entropy |
| State | Published - Aug 18 2019 |