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
Famous quotes containing the words mathematical and/or definition:
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)