Tossing Quantum Coins and Dice
This addresses foundational issues in quantum information processing for researchers, but it is incremental as it builds on existing frameworks.
The paper clarifies the distinction between quantum and classical conditional probabilities, showing that Lüders probability is not a generalization of classical conditional probability, with no concrete numerical results provided.
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 Lüders 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.