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arXiv 1607.07997quant-ph
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全量子相干性及其应用

Total quantum coherence and its applications

Chang-shui Yu, Yi-ren Yang, Bao-qing Guo

摘要:

量子相干性是量子力学最基本的特征。通常对它的理解取决于基的选择,即同一个量子态在不同的参考框架内相干性是不同的。为了揭示所有可能的相干性,我们用两种不同的方法给出了总的量子相干性测度。一个是优化最大基相关相干性与所有潜在的基地考虑,另一个是量化的状态和非相干态集之间的距离。有趣的是,基于相对熵和$l_2$范数的相干性度量在两种不同的方法中具有相同的形式。特别是,我们表明,基于非压缩$l_2$规范的措施也是一个很好的措施,从基地依赖的一致性不同。此外,我们还证明了所有的测度都是可解析计算的,并且具有所有的好的性质。提出了用多个量子态的拷贝代替全密度矩阵来检测这些相干测度的实验方案。通过对一类量子探测方案的研究发现,无论是单比特确定性量子计算方案(DQC 1)中的归一化迹,还是量子重叠测量方案(QOM)中的两态重叠,都可以用探测量子比特总相干的变化来描述.因此,非平凡的探测总是导致总相干的变化。

英文摘要:

Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To reveal all the potential coherence, we present the total quantum coherence measures in terms of two different methods. One is optimizing maximal basis-dependent coherence with all potential bases considered and the other is quantifying the distance between the state and the incoherent state set. Interestingly, the coherence measures based on relative entropy and $l_2$ norm have the same form in the two different methods. In particular, we show that the measures based on the non-contractive $l_2$ norm is also a good measure different from the basis-dependent coherence. In addition, we show that all the measures are analytically calculable and have all the good properties. The experimental schemes for the detection of these coherence measures are also proposed by multiple copies of quantum states instead of reconstructing the full density matrix. By studying one type of quantum probing schemes, we find that both the normalized trace in the scheme of deterministic quantum computation with one qubit (DQC1) and the overlap of two states in quantum overlap measurement schemes (QOM) can be well described by the change of total coherence of the probing qubit. Hence the nontrivial probing always leads to the change of the total coherence.

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