具有化学位移的液态核磁共振中幺正变换热态的原子纠缠
Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift
摘要：
最近，Yu，Brown和Chuang [Phys.Rev.A { \bf 71}，032341（2005）]研究了在液态核磁共振（NMR）中从幺正变换热态可获得的纠缠。他们的研究让我们深入了解了纠缠在液态NMR量子计算机中的作用。此外，他们还试图揭示混合态纠缠在量子计算中的作用。然而，他们假设对应于一个量子比特的每个核自旋的塞曼能量对所有人都有一个共同的值;没有化学位移。本文研究了一个含有化学位移的模型，利用正部分转置（PPT）判据，对任意的二分性，解析地导出了幺正变换热态纠缠的物理参数区域.我们考察了化学位移对可分性和不可分性边界的影响，发现它是可以忽略的。
英文摘要：
Recently, Yu, Brown, and Chuang [Phys. Rev. A {\bf 71}, 032341 (2005)] investigated the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance (NMR). Their research gave an insight into the role of the entanglement in a liquid-state NMR quantum computer. Moreover, they attempted to reveal the role of mixed-state entanglement in quantum computing. However, they assumed that the Zeeman energy of each nuclear spin which corresponds to a qubit takes a common value for all; there is no chemical shift. In this paper, we research a model with the chemical shifts and analytically derive the physical parameter region where unitary transformed thermal states are entangled, by the positive partial transposition (PPT) criterion with respect to any bipartition. We examine the effect of the chemical shifts on the boundary between the separability and the nonseparability, and find it is negligible.
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