What are pure states?

Some articles on states, pure states, state, pure state, pure:

Gelfand–Naimark Theorem
... In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a ... πf of A where f ranges over the set of pure states of A and πf is the irreducible representation associated to f by the GNS construction ... Krein extension theorem for positive linear functionals, there is a state f on A such that f(z) ≥ 0 for all non-negative z in A and f(−x* x) < 0 ...
Coherence (physics) - Quantum Coherence
... When the incident beam is represented by a quantum pure state, the split beams downstream of the two slits are represented as a superposition of the pure states representing each split beam ... do with two particles or Bell's inequalities relevant to an entangled state a 2-body state, a kind of coherence between two 1-body states.) The quantum description of imperfectly coherent paths ... A perfectly coherent state has a density matrix (also called the "statistical operator") that is a projection onto the pure coherent state, while a mixed ...
Bloch Sphere - A Generalization For Pure States
... The pure state space is by definition the set of 1-dimensional rays of Hn ... Then the pure state space of Hn can be identified with the compact coset space To prove this fact, note that there is a natural group action of U(n) on the set of states of Hn ... is continuous and transitive on the pure states ...
Multipartite Entanglement - Separability Characterization and Criteria - Pure States
... separability is given as follows The pure state of subsystems is fully -partite separable if and only if it can be written In order to check this, it is enough to compute reduced ... in the multipartite case, as only rarely multipartite pure states admit the generalized Schmidt Decomposition ... A multipartite state admits generalized Schmidt decomposition if, tracing out any subsystem, the rest is in a fully separable state ...
Hilbert Space - Applications - Quantum Mechanics
... formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states (more precisely, the pure states) of a quantum mechanical system are represented by ... In other words, the possible states are points in the projectivization of a Hilbert space, usually called the complex projective space ... on the system for example, the position and momentum states for a single non-relativistic spin zero particle is the space of all square-integrable functions, while the states for the spin of a single proton are ...

Famous quotes containing the words states and/or pure:

    The traveler to the United States will do well ... to prepare himself for the class-consciousness of the natives. This differs from the already familiar English version in being more extreme and based more firmly on the conviction that the class to which the speaker belongs is inherently superior to all others.
    John Kenneth Galbraith (b. 1908)

    God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his dimension known to himself alone.
    Marcus Minucius Felix (2nd or 3rd cen. A.D.)