Coherence cost for violating conservation laws
Coherence cost for violating conservation laws
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DOI：
10.1103/physrevresearch.2.043374
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发表时间：
2019-06
影响因子：
4.2
通讯作者：
H. Tajima;Naoto Shiraishi;Keiji Saito
中科院分区：
文献类型：
--
作者：
H. Tajima;Naoto Shiraishi;Keiji Saito
大自然对我们进行的操作施加了许多限制。这些限制中的许多可以解释为实现操作所需的{\it资源}。不同类型作业所需资源的分类和资源量的确定是物理学中的重要课题。在众多类型的运算中，酉运算是长期以来被隐式和显式地从资源的角度研究的最基本的运算之一。然而，如何确定资源并澄清根据保护法实施一般单一作业所需和足够的资源量，是一个长期悬而未决的问题。在本文中，我们为这一公开问题提供了一个解决方案。我们推导出一个渐近精确的等式，它阐明了在期望的误差范围内将量子相干作为资源来实现任意么正运算的必要条件和充分量。在这个等式中，所需的相干代价与实现误差和在期望的么正操作中违反守恒定律的程度渐近表示。我们还从相干性成本的角度讨论了几种物理情况下的物理基础。这项工作不仅解决了一个长期存在的关于么正控制的问题，而且澄清了在不对称资源论的范围内，对于么正信道的情况下量子信道的资源理论的关键问题。
Nature imposes many restrictions on the operations that we perform. Many of these restrictions can be interpreted in terms of {\it resource} required to realize the operations. Classifying required resource for different types of operations and determining the amount of resource are the crucial subjects in physics. Among many types of operations, a unitary operation is one of the most fundamental operation that has been studied for long time in terms of the resource implicitly and explicitly. Yet, it is a long standing open problem to identify the resource and to clarify the necessary and sufficient amount of resource for implementing a general unitary operation under conservation laws. In this paper, we provide a solution to this open problem. We derive an asymptotically exact equality that clarifies the necessary and sufficient amount of quantum coherence as a resource to implement arbitrary unitary operation within a desired error. In this equality, the required coherence cost is asymptotically expressed with the implementation error and the degree of violation of conservation law in the desired unitary operation. We also discuss the underlying physics in several physical situations from the viewpoint of coherence cost based on the equality. This work does not only provide a solution to a long-standing problem on the unitary control, but also clarifies the key question of the resource theory of the quantum channels in the region of resource theory of asymmetry, for the case of unitary channels.