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arXiv 2007.15592quant-ph
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量化Page-Wootters机制的资源：共享不对称性作为纠缠的相对熵

Quantifying resources for Page-Wootters mechanism: Shared asymmetry as relative entropy of entanglement

Rafael S. Carmo, Diogo O. Soares-Pinto

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发表信息：
Phys. Rev. A 103, 052420 (2021)
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摘要：

最近，量子钟的所谓Page-Wootters机制引起了一些关注。在使用更现代的技术来探索该机制的各种提议中，一些人选择使用量子信息视角，定义并使用信息度量来量化量子系统作为其他量子系统的参考系的能力。在这项工作中，我们探索了基于不对称性资源理论的提议，称为相互或共享不对称性，在这里感兴趣的情况下，这实际上相当于相干理论的方法：由$U(1)$紧群描述的量子参考系。我们将文献中关于共享不对称性和Page-Wootters机制的一些结果推广到更一般的情况，最终阐明了一个定理，该定理将二分态$ρ_{SR}$的共享不对称性与\textit{internal states} $ρ_M$在希尔伯特空间$\mathcal{H}_S\otimes\mathcal{H}_R$的电荷扇区上的纠缠的相对熵联系起来.利用这一结果，我们重新解释了Page-Wootters机制与纠缠的关系，也为进一步的研究开辟了一些途径。

英文摘要：

Recently, some attention has been given to the so-called Page-Wootters mechanism of quantum clocks. Among the various proposals to explore the mechanism using more modern techniques, some have chosen to use a quantum information perspective, defining and using informational measures to quantify how well a quantum system can stand as a reference frame for other quantum system. In this work, we explore the proposal based on resource theory of asymmetry, known as mutual or shared asymmetry, which actually is equivalent to the approach from coherence theory in the case of interest here: quantum reference frames described by the $U(1)$ compact group. We extend some previous results in literature about shared asymmetry and Page-Wootters mechanism to more general cases, culminating in the enunciation of a theorem relating shared asymmetry of a bipartite state $ρ_{SR}$ with the relative entropy of entanglement of \textit{internal states} $ρ_M$ on the charge sectors of the Hilbert space $\mathcal{H}_S\otimes\mathcal{H}_R$. Using this result we reinterpret the relation between Page-Wootters mechanism and entanglement and also open some paths to further studies.

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