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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  Negative base ten logarithm of the polarization $P$ as a function of the logarithm of the ratio of the energy level spacing to $k_{\sf  B}T$ for a one, four, sixteen and sixty-four spin pseudo-pure state obtained by cyclic averaging. For protons in a standard 500 MHz.\ spectrometer, $P \sim 10^{-5}$ at equilibrium. }}{14}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  The pairs of ${}^{13}{\sf  C}$-labeled chloroform spectra (carbon left, proton right) obtained by performing the four combinations of measurements ${\sf  A^CA^H}$, ${\sf  A^CB^H}$, ${\sf  B^CA^H}$ and ${\sf  B^CB^H}$ on the pseudo-pure form of Mermin's state ${{\mathchoice {\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$\displaystyle \Psi $}}{\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$\textstyle \Psi $}}{\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$\scriptstyle \Psi $}}{\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$\scriptscriptstyle \Psi $}}}}$. The spectra have been normalized by the height of the peak of the corresponding spin in the pseudo-pure ground state, and the horizontal axis is in kHz. The transitions of the peaks, from left to right, are $|0^{\sf  C}0^{\sf  H}\delimiter "526930B  \leftrightarrow |1^{\sf  C}0^{\sf  H}\delimiter "526930B $, $|0^{\sf  C}1^{\sf  H}\delimiter "526930B  \leftrightarrow |1^{\sf  C}1^{\sf  H}\delimiter "526930B $, $|0^{\sf  C}0^{\sf  H}\delimiter "526930B  \leftrightarrow |0^{\sf  C}1^{\sf  H}\delimiter "526930B $, $|1^{\sf  C}0^{\sf  H}\delimiter "526930B  \leftrightarrow |1^{\sf  C}1^{\sf  H}\delimiter "526930B $.}}{23}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  Experimental NMR data illustrating the decay of each of the product operators $\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^1$, $2\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^1\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^2$, $2\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^1\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^3$, $4\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^1\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^2 \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^3$, as functions of the time allowed for gradient diffusion (see text), together with the least-squares fits to their logarithms. The single and triple quantum coherences in $4\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^1\unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^2 \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$I$}_{\sf  z}^3$, (negative curves) have been plotted and fit separately. The sum of these data and the fits are also shown (topmost curve), which illustrates that error correction cancels the decay of the encoded state to first order as expected. \vspace  *{-12pt} }}{32}}
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