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Purification of quantum state : ウィキペディア英語版
Purification of quantum state
In quantum mechanics, especially quantum information, purification refers to the fact that every mixed state acting on finite-dimensional Hilbert spaces can be viewed as the reduced state of some pure state.
In purely linear algebraic terms, it can be viewed as a statement about positive-semidefinite matrices.
== Statement ==

Let ρ be a density matrix acting on a Hilbert space H_A of finite dimension ''n''. Then there exist a Hilbert space H_B and a pure state | \psi \rangle \in H_A \otimes H_B such that the partial trace of | \psi \rangle \langle \psi | with respect to H_B
:\operatorname \left( | \psi \rangle \langle \psi | \right )= \rho.
We say that | \psi \rangle is the purification of \rho.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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