Tossing Quantum Coins and Dice

TL;DR

This paper explores the process of tossing quantum coins and dice, highlighting the differences between quantum and classical probabilities, and clarifying their roles in quantum information and measurement theory.

Contribution

It clarifies the distinction between quantum and classical conditional probabilities and discusses their implications in quantum information processing.

Findings

Quantum probabilities cannot generally be reduced to classical ones.

Lüders probability is not a generalization of classical conditional probability.

Analogies between quantum measurement theory and decision theory are examined.

Abstract

The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is on the clarification of the difference between quantum and classical conditional probabilities. These probabilities are designed for characterizing different systems, either quantum or classical, and they, generally, cannot be reduced to each other. Thus the L\"{u}ders probability cannot be treated as a generalization of the classical conditional probability. The analogies between quantum theory of measurements and quantum decision theory are elucidated.