# Talk:Quantized baker map

The article is well written and comprehensive. A few suggestions for the authors' consideration, some in the nature of minor typos.

1. I think the baker map (baker's map?) was invented by E. Hopf (1937, Ergodic Theory). This seems to be missing from the Wiki entry for the bakers map as well, and it will be nice to have this historical perspective.

2. In the "Periodic orbits" part, I think there is an extra "epsilon" in the string "nu". Also "n_{\nu}" can be equal to zero. I think in many places thereon there is one more bit than necessary in the strings.

3. In the same "Periodic orbits" part the figure seems to include only "primitive/prime" periodic orbits, but this is not indicated in the text.

4. It will be nice if the quantum map B is somehow highlighted (box?, bold?) and the simplicity of it, being constructed out of finite Fourier transforms be highlighted. As the QFT algorithm is easy to implement, the quantum baker on a qubit machine is realizable/realized?

5. Speaking of "realizations", consider including: Phys. Rev. A 61, 012304 (1999) Linear optics simulations of the quantum baker’s map.

6. The equation for exponential increase of the number of periodic orbits is likely to be confusing: some brackets may help.

7. The bakers map is hyperbolic, while nonhyperbolic and eventually hyperbolic bakers maps and their quantizations have been studied as the class of "lazy baker maps". Annals of Physics Volume 226, Issue 2, September 1993, Pages 350–373.

8. Quantum Multi-baker maps were studied as early as 1994 in:
Journal of Statistical Physics
October 1994, Volume 77, Issue 1-2, pp 311-344
Relaxation and localization in interacting quantum maps

9. Perhaps worth mentioning explicitly that the BVS quantization's (the "canonical quantum baker") spectra is not solvable exactly despite its apparent simplicity. Also that there are many random matrix like features that one would expect for generic systems. In this sense it is quite different from its relative the "quantum cat map" that is nongeneric and is "solvable" is some ways. Also the nongenericity of dimensions that are powers of 2 (pure qubits) maybe mentioned in this context. The existence of an approximate ansatz for a class of states in this case that involves simply adding the automatic Thue-Morse sequence with its Fourier transform maybe worth mentioning as well?