Picturing Quantum Processes: typos, omissions and further developments

Improvements:

• [Prop 4.13 on page 91, Eqs (4.11), Exercise 4.14 on page 92 and Theorem 4.19 on page 93]: It suffices to consider only two equations in Prop 4.13 and Eqs (4.11), in order for Theorem 4.19 to hold. In particular, Prop 4.13 can be restated as: Special thanks Ciprian Stirbu and Louis Mahon for pointing this out! Oh dear, this was a pretty bad one...

• [computation (5.7) on page 165]: The middle step is not needed since the 3rd equation follows from the 1st by (4.1), just like in the proof of Theorem 5.18. That said, the explicit use of the transpose here is kind of cute.
Typos:

• [page 197]: The title of section 5.2.4 should be Matrices of String diagrams, not the other way around..

• [page 577]: In the definition of even-parity function the values 0 and 1 need to be swapped.

• [page 642]: The presentation of the basis states at the top of the page should be: In the two sets of diagrams at the bottom of the page all pi/2 have to be pi: This is a pretty bad page, and it is in the summarising chapter. :(

• [page 666]: The triangle on the right in the computation has the wrong two-element subset, and should have been {1, 4}.

• [page 666]: We just repeat the page number for the hell of it...
Omissions:

• [page xvii]: Thanks to Marietta Stasinou, Ciprian Stirbu and Louis Mahon for pointing out typos in the published version!

• [proof of Theorem 5.32 on page 175]: In the last line, the basis is an ONB because of Proposition 5.10.

• [Ch. 9, Historical Notes]: In Lafont's 2003 paper Towards an algebra of boolean circuits the structure of a Hopf-algebra also occurred. However, the nodes were in this case no spiders and hence weren't really able to do much milage.

• [Ch. 12, Historical Notes]: Brickwork states were introduced and used to establish universality with only XY-plane measurements in Broadbent, Fitzsimons and Kashefi's 2009 paper Universal Blind Quantum Computation.
Further developments:

• [Sec. 4.3.1]: This section included an indication of the properties of the adjoint beyond the fact that it is merely a vertical reflection. Now the dagger has been axiomatised by Selby and Coecke in arXiv:1606.05086, and this axiomatisation constitutes a part of a process-theoretic reconstruction of quantum theory by Selby, Scandolo and Coecke in arXiv:1802.00367.

• [Sec. 9.4.6]: This section is concerned with where we stood with ZX-calculus, but this is not anymore where we now stand. In fact, ZX-calculus has been completed! This went in a number of steps. First, Completeness of Clifford+T maps was achieved by Jeandel, Perdrix and Vilmart in arXiv:1705.11151. This proof relied on the then known completeness results by Hadzihasanovic for the Z/W-calculus which we briefly touched upon in sec. 13.3.3. Meanwhile, Hadzihasanovic has shown general completeness of Z/W-calculus in his DPhil thesis arXiv:1709.08086, and based on that result, Ng and Wang were able in arXiv:1706.09877 to construct an extension of ZX-calculus that is generally complete. There are a number of follow-up papers by the same authors aimed at improving the rule set.

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