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After a brief introduction to Probability Bracket Notation (PBN), indicatoroperator and conditional density operator (CDO), we investigate probabilityspaces associated with various quantum systems: system with one observable(discrete or continuous), system with two commutative observables (independentor dependent) and a system of indistinguishable non-interacting many-particles.In each case, we derive unified expressions of conditional expectation (CE),conditional probability (CP), and absolute probability (AP): they have the sameformat for discrete or continuous spectrum; they are defined in both Hilbertspace (using Dirac notation) and probability space (using PBN); and they may beuseful to deal with CE of non-commutative observables.

Probability Bracket Notation: the Unified Expressions of Conditional Expectation and Conditional Probability in Quantum Modeling