Mathematical Definition
The basic definition in quantum probability is that of a quantum probability space, sometimes also referred to as an algebraic or noncommutative probability space.
- Definition : Quantum probability space.
A pair (A, P), where A is a *-algebra and P is a state, is called a quantum probability space.
This definition is a generalization of the definition of a probability space in Kolmogorovian probability theory, in the sense that every (classical) probability space gives rise to a quantum probability space if A is chosen as the *-algebra of bounded complex-valued measurable functions on it.
The projections p ∈ A are the events in A, and P(p) gives the probability of the event p.
Read more about this topic: Quantum Probability
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