Before revision:  One of the many potential applications is in finance: we associate the signal to a random payoff and price a financial derivative within the modulated information approach. It turns out that the price of a vanilla optioncan be expressed by a weighted sum of option values based on the possible state configurations at option expiry.
After revision:  One of the many potential applications is in finance: we associate the signal to a random payoff and price a financial vanilla option, which we prove is expressed by a weighted sum of option values based on the possible state configurations at option expiry.