as a state retrieved from previous observations). Additionally we determine, within the context of our model, the quality of the spectra and the number of useful retrievable atmospheric properties. This work represents the first attempt at determining the amount of useful information that can be retrieved from typical exoplanet spectra. Furthermore, this paper represents the first attempt at using information theoretic limits for retrievals assuming certain instrument capabilities (such as R and S/N). Ultimately, the theory is general and enables prediction of the advances that can be made with improvements in instrumentation and via more prudent choice of spectral ranges.

In $\S$[2]{} we outline the basics of the classic retrieval theory of Rodgers (2000). We first test the technique on an artificial dataset and explore how the number of retrievable parameters depends on $R$ and $S/N$ and discuss how these can be optimized to maximize the usefulness of a measurement in $\S$3. We then apply these techniques to the well studied HD189733b dayside emission spectra in $\S$4. This is followed by a discussion and conclusions in $\S$5.

Method
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Retrieval Theory
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The retrieval problem is well known in the field of Earth atmospheric studies (Rodgers 1976, Chahine 1968, Twomey 