- #1
jeebs
- 325
- 4
Hi,
this is probably a straightforward question over something simple but it's confusing me. I don't get what the difference is between a mixed state, a superposition and a pure state. I'm looking through my notes about density operators and it's talking about a qubit system where [tex] |0> = \left(\begin{array}{c}1&0\end{array}\right) [/tex] and [tex] |1> = \left(\begin{array}{c}0&1\end{array}\right) [/tex].
It then goes on to talk about the system being in state [tex] |+> = \frac{1}{\sqrt{2}}(|0> + |1>) [/tex], but it calls it a "pure state". This does not look pure to me, I would have called |0> and |1> the pure states, and |+> superposition of the two.
Using the basis { |+>, |-> }, where [tex] |-> = \frac{1}{\sqrt{2}}(|0> - |1>) [/tex], the density operator can be found: [tex] \rho = \left(\begin{array}{cc}1&0\\0&0\end{array}\right) [/tex].
The notes say that "the statistical mixture of pure states giving rise to the density operator is called a mixed state". |+> certainly looked like a statistical mixture of |0> and |1> to me. Is there a difference between a mixed state and a superposition?
this is probably a straightforward question over something simple but it's confusing me. I don't get what the difference is between a mixed state, a superposition and a pure state. I'm looking through my notes about density operators and it's talking about a qubit system where [tex] |0> = \left(\begin{array}{c}1&0\end{array}\right) [/tex] and [tex] |1> = \left(\begin{array}{c}0&1\end{array}\right) [/tex].
It then goes on to talk about the system being in state [tex] |+> = \frac{1}{\sqrt{2}}(|0> + |1>) [/tex], but it calls it a "pure state". This does not look pure to me, I would have called |0> and |1> the pure states, and |+> superposition of the two.
Using the basis { |+>, |-> }, where [tex] |-> = \frac{1}{\sqrt{2}}(|0> - |1>) [/tex], the density operator can be found: [tex] \rho = \left(\begin{array}{cc}1&0\\0&0\end{array}\right) [/tex].
The notes say that "the statistical mixture of pure states giving rise to the density operator is called a mixed state". |+> certainly looked like a statistical mixture of |0> and |1> to me. Is there a difference between a mixed state and a superposition?