electromagnetic radiation - What does electric field of unpolarized light look like when measured?

When we talk about fermions in mixed state, we say that their state can't be described by a wavefunction and just compute all the probabilities using density matrix. That's OK because the wavefunctions aren't observable. But the analogous function for photons (which is admittedly not quite a wavefunction, but still has many properties of it) is observable — electromagnetic tensor or even just electric and magnetic fields.

Now I might just say that we can't use electric and magnetic fields to describe unpolarized light, but observability of these quantities makes me feel that this is wrong.

So my question is, what would electric field of unpolarized EM wave look like when measured (assuming low enough frequencies to be measurable)? Will it just fluctuate wildly in direction, remaining regularly changing in amplitude?