  Faraday rotation is one way to realize quantum non-demolition measurement of
electron spin in quantum dots. To describe Faraday rotation, semiclassical
models are typically used, based on quantized electron spin states and
classical electromagnetic fields. Such treatments neglect the entanglement
between electronic and photonic degrees of freedom that produce intrinsic
quantum noise, limiting the ultimate sensitivity of this technique. We present
a fully quantum-mechanical description of Faraday rotation, and quantify this
intrinsic noise. A method for measuring the purity of a given spin state is
suggested based on this analysis.
