Entropy Loss of KDFs

Am I losing any entropy when using KDFs, such as the ones in NIST Special Publication 800-108?
For example, can I derive 128-bit session keys from a (uniformly random) 128-bit master key?

When you use a PRF to derive a key, there is the potential for collisions. If you derived a 128-bit key from each possible 128-bit number, you'd expect some of them to collide. Specifically, you'd expect only about 63% of all the inputs ($1-e^{-1}$) to appear as outputs.
In general, if you use a PRF to derive an $n$-bit key from one with $k$ bits of entropy, the resulting key will have at least $\min(n, k) - 1$ bits of entropy, approaching $\min(n, k)$ when $k \ll n$ or $k \gg n$.
• @owlstead, the question was $128 \mapsto 128$, but sure, added a paragraph. – otus Aug 19 '14 at 17:57
• Thanks for the answer. Can you add a reference for $1-e^{-1}$? – Konny Aug 20 '14 at 8:56