Paper VII: Quantum Seed Calculus

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (2.25,4.2) {$T$ at $e^{-2\tau}=1/2$};
4 \path[draw=black!30,fill=black!8] (1.1,2.35) rectangle (2.25,3.5);
5 \node[font=\small,align=center,font=\small] at (1.675,2.925) {$\frac{3}{4}$};
6 \path[draw=black!30,fill=black!8] (2.25,2.35) rectangle (3.4,3.5);
7 \node[font=\small,align=center,font=\small] at (2.825,2.925) {$\frac{1}{4}$};
8 \path[draw=black!30,fill=black!8] (1.1,1.2) rectangle (2.25,2.35);
9 \node[font=\small,align=center,font=\small] at (1.675,1.775) {$\frac{1}{4}$};
10 \path[draw=black!30,fill=black!8] (2.25,1.2) rectangle (3.4,2.35);
11 \node[font=\small,align=center,font=\small] at (2.825,1.775) {$\frac{3}{4}$};
12 \node[font=\small,align=center,font=\small] at (10.35,4.2) {$ZTZ$ in another basis};
13 \path[draw=black!30,fill=black!8] (9.2,2.35) rectangle (10.35,3.5);
14 \node[font=\small,align=center,font=\small] at (9.775,2.925) {$\frac{3}{4}$};
15 \path[draw=black!30,fill=black!8] (10.35,2.35) rectangle (11.5,3.5);
16 \node[font=\small,align=center,font=\small] at (10.925,2.925) {$- \frac{1}{4}$};
17 \path[draw=black!30,fill=black!8] (9.2,1.2) rectangle (10.35,2.35);
18 \node[font=\small,align=center,font=\small] at (9.775,1.775) {$- \frac{1}{4}$};
19 \path[draw=black!30,fill=black!8] (10.35,1.2) rectangle (11.5,2.35);
20 \node[font=\small,align=center,font=\small] at (10.925,1.775) {$\frac{3}{4}$};
21 \node[font=\small,align=center,font=\small] at (6.5,2.4) {Both have\\spectrum $\{1,1/2\}$.};
22 \node[font=\small,align=center,font=\small] at (7,0.4) {Positive-definite operator: $v^*Tv>0$ for $v\ne0$. Not an entrywise test.};
23 \end{tikzpicture}

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