I Entanglement, Mixed or Pure State?

[stephen8686]

I have a source that says when two particles are entangled, we must describe them using the density operator because it is a mixed state. But I have another source that says that the singlet state of two spins is an entangled state, but that has a wavefunction. So could someone explain what I am misunderstanding? Are all entangled states mixed states or only some?

 

[StevieTNZ]

Would be helpful if you clarified what your sources are.

 

[Nugatory]

when two particles are entangled, we must describe them using the density operator because it is a mixed state.

When two particles are entangled the state of either one is a mixed state that can only be described with a density operator. (in the most convenient basis the density matrix for either particle is $diag(1/2,1/2)$, equal probability of measuring spin-up or spin down).

But I have another source that says that the singlet state of two spins is an entangled state, but that has a wavefunction.

The singlet state is the state of a single quantum system that will produce measurement results at two spatially separated detectors. It is a pure state with a wave function - but it is not the state of either particle considered in isolation.

 

[Demystifier]

I have a source that says when two particles are entangled, we must describe them using the density operator because it is a mixed state. But I have another source that says that the singlet state of two spins is an entangled state, but that has a wavefunction. So could someone explain what I am misunderstanding? Are all entangled states mixed states or only some?

To rephrase what @Nugatory said, the state that simultaneously describes both particles together is pure, while the state that describes any of the particles alone is mixed.