矩阵元转移的量子限制
Quantum restrictions on transfer of matrix elements
摘要：
我们讨论了量子力学对矩阵元素从一个系统转移到另一个系统的过程所施加的限制。这与部分状态转移的各种过程（量子通信、间接测量、偏振转移、{ \it等}）相关。给定两个系统A和B，初始密度算子分别为$λ$和$r$，我们考虑了大多数一般的相互作用，这导致未知$λ$的某些矩阵元素转移到B的终态${\widetilde r}$的矩阵元素。我们发现，这个过程导致消除记忆的转移（或某些其他）矩阵元素的最终状态的A。如果转移一个对角矩阵元素：${\widetilde r}_{aa}=λ_{aa}$，则从A的最终密度算子中完全消除了对每个非对角元素$λ_{a\not=b}$的存储。非对角元素${\widetilde r}_{ab}=λ_{ab}$的传递消除了对角元素$λ_{aa}$和$λ_{bb}$的存储，而保留了关于它们的和$λ_{aa}+λ_{bb}$的存储。而且，关于$λ_{ab}$本身的记忆从A的最终状态中完全消除了。将这些设置推广到非理想传输会带来传输质量和保留内存量之间的权衡。这种权衡是通过系统独立的不确定性关系表示的。
英文摘要：
We discuss restrictions imposed by quantum mechanics on the process of matrix elements transfer from the one system to another. This is relevant for various processes of partial state transfer (quantum communication, indirect measurement, polarization transfer, {\it etc}). Given two systems A and B with initial density operators $λ$ and $r$, respectively, we consider most general interactions, which lead to transferring certain matrix elements of unknown $λ$ into those of the final state ${\widetilde r}$ of B. We find that this process leads to eliminating the memory on the transferred (or certain other) matrix elements from the final state of A. If one diagonal matrix element is transferred: ${\widetilde r}_{aa}=λ_{aa}$, the memory on each non-diagonal element $λ_{a\not=b}$ is completely eliminated from the final density operator of A. The transfer of a non-diagonal element: ${\widetilde r}_{ab}=λ_{ab}$ eliminates the memory on the diagonal elements $λ_{aa}$ and $λ_{bb}$, while the memory about their sum $λ_{aa}+λ_{bb}$ is kept. Moreover, the memory about $λ_{ab}$ itself is completely eliminated from the final state of A. Generalization of these set-ups to non-ideal transfer brings in a trade-off between the quality of the transfer and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations.
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