T^{-}(y)
\end{array}$$ for deterministic case. Where we write $A(y)\varsubsetneq B(y)$ if $A(y)\subseteq B(y)$ holds for all $y$ but there exists some $y$ such that $A(y)\neq B(y)$; while by $A(y){\ensuremath        {\underset{\mbox{\sout{\tiny{\,?\,}}}}{\subset}}}B(y)$ we indicate that whether or not there exists $y$ such that $A(y)\neq B(y)$ is still open, although $A(y)\subseteq B(y)$ always holds for all $y$.

From the above two diagrams, the remaining questions for further study are:

1). Whether or not $\overline{T^{\lambda}(y)}= T^{\lambda-}(y)$ (or equivalently, $\overline{M^{\lambda}(y)}= M^{\lambda-}(y)$ ) for any $y$ and $\lambda\leq 1$. In other words, whether or not the function $T^{\lambda}(y)$ (or $M^{\lambda}(y)$) is ‘almost’ left continuous at any $\lambda\leq 1$.

2). Whether or not $\overline{T(y)}= \overline{M(y)}$ (or equivalently, $T(y)^\circ= M(y)^\circ$) for any $y$. That is, whether or not catalyst-assisted transformation and multiple-copy transformation are also geometrically equivalent in deterministic setting.

ACKNOWLEDGMENTS {#acknowledgments .unnumbered}
===============

The authors thank the colleagues in the Quantum Computation and Quantum Information Research Group for useful discussion. This work was partly supported by the Natural Science Foundation of China (Grant Nos. 60503001, 60321002, and 60305005), and by Tsinghua Basic Research Foundation (Grant No. 052220204). R. Duan acknowledges the financial support of Tsinghua University (Grant No. 052420003).


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abstract: |
    Background

    :   Measurement of the fusion cross-section for neutron-rich light nuclei is crucial in ascertaining if fusion of these nuclei occurs in the outer crust of a neutron star.

    Purpose

    :   Measure the fusion excitation function at near-barrier energies for the $^{19}$O + $^{12}$C system. Compare the experimental results with the fusion excitation function of $^{18}$O + $^{12}$C and $^{16}$O + $^{12}$C.

    Method

    :   A beam of $^{19}$O, produced via the $^{18}$O(d,p) reactio