99 pages!

I've moved on to the Schur half of the thesis, which has been cruising along well. Chap 6 is the background on rep. theory/Schur duality, Chap 7 is on applications to information theory and Chap 8 is algorithms. 6 and 7 are done! as is 3/5 of chap 8! All that remains is to incorporate these scrappy notes.

And check out the dynamite concluding section of chapter 7, summarizing my new contributions on using the Schur transform in quantum information theory.

Conclusions

The results of this chapter should be thought of laying the groundwork for a quantum analogue of joint types. Although many coding theorems have been proved for noisy states and channels without using this formalism, hopefully joint quantum types will give proofs that are simpler, more powerful, or not feasible by other means. One problem for which the technique seems promising is the Quantum Reverse Shannon Theorem\cite{BDHSW05}, in which it gives a relatively simple method for simulating a noisy quantum channel on arbitrary sources. It remains to be seen where else the techniques will be useful.

I rule.