Qbit pure vs mixed state space

In summary, the distinction between pure and mixed state spaces in quantum mechanics revolves around the representational fidelity of quantum states. Pure states are described by a single wave function and represent maximum knowledge about a quantum system, while mixed states arise from statistical mixtures of pure states, indicating a lack of complete information. Mixed states are typically represented by density matrices, allowing for the modeling of systems influenced by noise or entanglement with the environment. Understanding these concepts is crucial for applications in quantum computing and quantum information theory.
  • #36
cianfa72 said:
A vector is an eigenvector for an operator regardless of the picked basis.
Yes, but it is one of the basis vectors in only one basis.

cianfa72 said:
it could be for example in the form $$\ket{0}=\begin{bmatrix} 1 \\ 0 \end{bmatrix}$$
Yes, it would be a basis vector in this basis, but not in any other basis.
 

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