I'm aware that unpolarized light can be represented by a mixed state $\frac{1}{2}(|x\rangle\langle x| + |y\rangle\langle y |)$. It bothers me that in this framework, unpolarized light is a symptom of our classical aleatoric uncertainty. I do remember my professor in my undergraduate quantum physics class telling me once that "unpolarized light is in the superposition of all polarizations". But this doesn't seem to be true? Is there a way to sensibly model unpolarized light as a purely quantum phenomenon or is unpolarization simply a matter of classical probability?

I was thinking that one could just brute force model unpolarized light as a normalized vector on $L^2(PGL(2,\mathbb R))$ for all the possible orientations, but that just opens up other questions - why don't we see other continuous superpositions of polarizations - why is unpolarized light special? Maybe it is silly to want unpolarized light to make sense in the world of purely quantum statistics - but it bothers me that unpolarized light involves an inherently different sort of uncertainty than say, a superposition of horizontal and vertically polarized light.

  • $\begingroup$ Circular polarized light is a superposition of polarizations! And be careful of superpositions ..... 2 photons travelling in sync and out of phase have zero EM field classically but of course in QM the photons are still present! $\endgroup$ Commented Oct 22, 2023 at 4:03
  • $\begingroup$ Any pure state can be described as a superposition by taking a different basis right? But I dont see how one would model unpolarized light as a pure state of a single photon $\endgroup$ Commented Oct 23, 2023 at 0:17
  • $\begingroup$ Yes a single photon is difficult to model from a polarization perspective ... you would need to define an arbitrary E vector (say up or north ) and theorize it relative to that. Not sure if scientists need this, they just assume polarization properties for different apparatuses etc. $\endgroup$ Commented Oct 23, 2023 at 0:51
  • $\begingroup$ Yeah the density matrix formalism works just fine, it just bothers me that this necessarily requires classical stochasticity $\endgroup$ Commented Oct 23, 2023 at 1:54

1 Answer 1


Unpolarized light in quantum mechanics is described by a mixed state. That is a probability for a photon to be in either of 2 quantum states. This can arise, for example, if the photon is correlated, i.e. entangled, with other degrees of freedom that you don't measure. In that case the cross terms in a superposition which would normally cause interference have the other degrees of freedom in different states so they give zero. If you know you aren't going to measure those other degrees of freedom, the photon properties can be described by the reduced density matrix, which describes this mixed state.


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