State
Mathematical object that can be used to deter-mine the probability associated with the out-comes of any measurement that may be per-formed on a system prepared by the given preparation.
However, we do not need to measure all possible probability measurements to determine the state of a system.
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K (degrees of freedom): minimum number of probability measurements required to determine the state of a system, i.e., number of real parameters re-quired to specify the state.
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N (dimension): maximum number of states that can be reliably distinguished from one another in a single shot measurement.
Axioms
1.
Probabilities
2.
Simplicity:
3.
Subspaces: If state of a system subspace
4.
Composite systems:
5.
Continuity: a continuous reversible transformation on a system between anytwo pure states of that system