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Encyclopedia > 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 statistically 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

In the density operator formalism, a pure state is an idempotent transformation, following the properties of projection operators

ρ = ρ2

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.


  Results from FactBites:
 
Pure qubit state (259 words)
In quantum information processing, a pure qubit state is a linear superposition[?] of two basis states, conventionally written 0⟩ and 1⟩ (ket 0 and ket 1).
A pure qubit state is often written as the sum a 0⟩ + b 1⟩, or as a column vector (a, b) where a and b are the complex amplitudes associated with 0⟩ and 1⟩, respectively.
If the state 0⟩ is measured, a is changed to a magnitude of 1 and b is changed to a magnitude of 0 (see magnitude of complex numbers).
PlanetMath: state (190 words)
A state is pure if it is not a convex combination of two other states.
Pure states are the extreme points of the convex set of states.
This is version 5 of state, born on 2003-08-11, modified 2006-11-21.
  More results at FactBites »


 

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