arXiv quant-ph/98070911998-07quant-ph

一般隐形传态通道、单重态分数和准蒸馏

General teleportation channel, singlet fraction and quasi-distillation

Pawel Horodecki, Michal Horodecki, Ryszard Horodecki

备注：: RevTeX, 14 pages, proposition in Sec. VI has been corrected, many minor corrections

摘要：

本文证明了一个关于量子隐形传态的最佳保真度$f_{max}$与利用保迹LQCC作用量（局域量子和经典通信）所能达到的最大单态分数$F_{max}$之间的直接关系的定理。对于给定的作用于$C^d\otimes C^d$的二分态，我们有$f_{max}= {F_{max}d+1\over d+1}$。我们假设完全一般的隐形传态方案（对未知态的第三个粒子和对的迹保持LQCC作用）。证明涉及到量子信道和一类二分态之间的同构。我们还利用技术的$U\otimes U^*$旋转状态（随机应用上述形式的幺正变换）和介绍类似的旋转通道。我们通过证明{ \it any}束缚纠缠态并不能提供比纯经典信道更好的隐形传态保真度来说明该定理的威力。随后，我们应用我们的工具，所谓的结论性隐形传态的问题，然后减少到单态分数的最佳结论性增加的问题。我们提供了一个状态的例子，其中Alice和Bob没有机会通过LQCC作用获得完美的单态，但仍然可以以非零概率获得任意接近于1的单态分数。我们表明，状态的轻微修改有一个阈值，不能再超过的单重态分数。

英文摘要：

We prove a theorem on direct relation between the optimal fidelity $f_{max}$ of teleportation and the maximal singlet fraction $F_{max}$ attainable by means of trace-preserving LQCC action (local quantum and classical communication). For a given bipartite state acting on $C^d\otimes C^d$ we have $f_{max}= {F_{max}d+1\over d+1}$. We assume completely general teleportation scheme (trace preserving LQCC action over the pair and the third particle in unknown state). The proof involves the isomorphism between quantum channels and a class of bipartite states. We also exploit the technique of $U\otimes U^*$ twirling states (random application of unitary transformation of the above form) and the introduced analogous twirling of channels. We illustrate the power of the theorem by showing that {\it any} bound entangled state does not provide better fidelity of teleportation than for the purely classical channel. Subsequently, we apply our tools to the problem of the so-called conclusive teleportation, then reduced to the question of optimal conclusive increasing of singlet fraction. We provide an example of state for which Alice and Bob have no chance to obtain perfect singlet by LQCC action, but still singlet fraction arbitrarily close to unity can be obtained with nonzero probability. We show that a slight modification of the state has a threshold for singlet fraction which cannot be exceeded anymore.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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