量子纠缠探测方案能改进搜索吗？
Can Quantum Entanglement Detection Schemes Improve Search?
摘要：
量子计算，特别是Grover算法，已经引起了极大的兴趣，因为它允许在搜索过程中获得二次加速。用于$N$元素数据库的经典搜索过程最多需要$O(N)$时间复杂度。Grover的算法通过振幅放大方案能够在$O(\sqrt{N})$时间内以高概率找到解。在这项工作中，我们从经典计算和量子计算中汲取元素，开发了一种基于量子纠缠检测方案的替代搜索方案。2002年，Horodecki和Ekert提出了一种直接检测量子纠缠的有效方法。我们对量子搜索的提议结合了量子纠缠检测和纠缠诱导算子。Grover的量子搜索依赖于在应用幺正演化后测量量子叠加。我们偏离了标准的方法，专注于微调一个酉算子，以推断的解决方案与确定性。我们的建议牺牲空间的速度，并依赖于线性正映射$Λ$的数学性质还没有操作的特点。这样的$Λ$是否可以容易地确定仍然是一个悬而未决的问题。
英文摘要：
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most $O(N)$ time complexity. Grover's algorithm is able to find a solution with high probability in $O(\sqrt{N})$ time through an amplitude amplification scheme. In this work we draw elements from both classical and quantum computation to develop an alternative search proposal based on quantum entanglement detection schemes. In 2002, Horodecki and Ekert proposed an efficient method for direct detection of quantum entanglement. Our proposition to quantum search combines quantum entanglement detection alongside entanglement inducing operators. Grover's quantum search relies on measuring a quantum superposition after having applied a unitary evolution. We deviate from the standard method by focusing on fine-tuning a unitary operator in order to infer the solution with certainty. Our proposal sacrifices space for speed and depends on the mathematical properties of linear positive maps $Λ$ which have not been operationally characterized. Whether such a $Λ$ can be easily determined remains an open question.
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