What Are the Key Questions Surrounding Quantum Decoherence?

[A. Neumaier]

what an improper mixed density operator is. Its 100% quantum.

No. Mixing (unlike superposition) is both a classical and a quantum phenomenon.

Classical mechanics is (in terms of its kinematics) just the special case of quantum mechanics where all operators define superselection sectors. Thus the only pure states considered are those from an orthonormal basis, and the only operators considered are diagonal and hence have fixed (eigen)values in each allowed pure state.

A mixed state composed of orthogonal pure states (which is what one has in classical mechanics) is just a positive semidefinite diagonal density matrix with trace 1 - i.e., a traditional probability distribution.

 

[A. Neumaier]

Assuming our world is indeed governed by quantum laws and the wavefunction of the universe is pure (and the universe doesn't interact with anything, so that its time evolution is unitary), can proper mixed states even exist?

Yes, since we usually only consider small localized subsystems, and the mixing occurs through restriction to the subsystem (typically by trace formation). The mixed state is the usual situation - it requires extreme care to create a pure state, and can be done only if the subsystem considered only has very few and discrete degrees of freedom.

Whether the universe is in a pure or a mixed state we cannot tell since we observe only little pieces of it.

 

[bhobba]

No. Mixing (unlike superposition) is both a classical and a quantum phenomenon.

True.

Thanks
Bill