- #1

Trixie Mattel

- 29

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So, in my mind the differences lie in knowing the states that the system could end up in, and also the difference in the probabilities.

Is this thinking correct:

For a mixed state, there exists classical randomness. So for example some machine prepares a state

|ψ1> and that is the desired state I would like to get. However the machine is faulty and also prepares some state |ψ2>. The probability of getting |ψ1> is P1 and the probability of state |ψ2> being prepare is 1-P1.

The probabilities here are classical. Also |ψ2> is some state, made by the faulty machine, that I am not really aware of. I am not sure of its characteristics. Its prepared due to classical randomness. And so I get a mixed state of P1|ψ1> + P2|ψ2>Then there's for example a particle. Which can be in spin up or spin down, |0> and |1> respectively.

Here I am aware of the possible state the particle may end up in and the characteristics of those states.

However I can not be sure of which state the particle is in until i make a measurement (the wavefunction collapses) and then it will be in one state or the other. Here in QM we can think of the particle, before measurement as existing in a quantum superposition of both states. α|0> + β|1>

where α and β are not classical probabilities, they are quantum probability amplitudes. And also we can think of this quantum superposition of pure states as just another pure state before measurement.Is that a correct way of thinking of the difference between mixed states and quantum superposition?

Also, to be in quantum superposition, is it a necessity that the superimposed states are eigenstates of some hermitian operator??Thank you very much