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arXiv 0807.4490quant-ph
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纠缠在混合态量子计算中的作用研究

Studies on the Role of Entanglement in Mixed-state Quantum Computation

Animesh Datta

备注：
PhD thesis, defended in June 2008. 130 pages, 14 figures. arXiv admin note: text overlap with arXiv:quant-ph/0201143 by other authors
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摘要：

在这篇论文中，我研究了量子纠缠在混合态量子计算中的作用。我们考虑的模型是DQC 1或“一个量子比特的幂”模型。我表明，有最小的二分纠缠在一个典型的实例中的DQC 1电路，甚至把一个上限上的可能的纠缠量。然而，这种有限的纠缠并不意味着系统是经典可模拟的。DQC 1系统的一个典型实例的矩阵乘积状态（MPS）算法需要指数经典资源。这暴露了量子系统中纠缠量和纯非经典关联量之间的差距。我认为，这个缺口可以用量子不和谐来填补。我在DQC 1电路的一个典型实例中计算了它，发现不和谐的数量是该大小的系统的最大可能不和谐的一个常数。这允许将量子不和谐解释为驱动混合态量子计算的资源。我也把量子不和谐作为一个独立的兴趣量来研究。通过一个易于理解的例子研究了它在纠缠分布现象中的作用。本文还讨论了复杂性类P、BQP和DQC 1之间的关系。额外的材料是DQC 1模型，琼斯多项式和统计力学之间的连接。本文最后讨论了与DQC 1模型、量子不和谐及其在量子信息科学中的应用范围有关的几个开放性问题。

英文摘要：

In this thesis, I look at the role of quantum entanglement in mixed-state quantum computation. The model we consider is the DQC1 or `power of one qubit' model. I show that there is minimal bipartite entanglement in a typical instance of the DQC1 circuit and even put an upper bound on the possible amount of entanglement. This limited amount of entanglement, however, does not imply that the system is classically simulatable. A matrix product state (MPS) algorithm for a typical instance of the DQC1 system requires exponential classical resources. This exposes a gap between the amount of entanglement and the amount of purely nonclassical correlations in a quantum system. This gap, I suggest, can be filled by quantum discord. I calculate it in a typical instance of the DQC1 circuit and find that the amount of discord is a constant fraction of the maximum possible discord for a system of that size. This allows an interpretation of quantum discord as the resource that drives mixed-state quantum computation. I also study quantum discord as a quantity of independent interest. Its role in the phenomenon of entanglement distribution is studied through an easily comprehensible example. This thesis also contains discussions on the relation between the complexity classes P, BQP and DQC1. Additional material is presented on the connections between the DQC1 model, Jones polynomials and statistical mechanics. The thesis concludes with a discussion of a few open problems related to the DQC1 model, the quantum discord and their scope in quantum information science.

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。

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