The Pure state reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Pure state

The term pure state refers to several related concepts in physics, particularly quantum mechanics and in functional analysis. In quantum mechanics a pure state S of a quantum system is a state represented by a density operator which cannot be decomposed as a randomization of two statisticaly different statistical ensembles. Mathematically this means S is an extreme point in the set of states. Such states are given in Dirac bra-ket notation by

A pure state on a C*-algebra A is a state which is an extreme point of the set of all states on A. By properties of the GNS construction these states correspond to irreducible representations of A.

The states of the C*-algebra of compact operators K(H) correspond exactly to the density operators and therefore the pure states of K(H) are exactly the pures states in the sense of quantum mechanics.

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