Entropic Energy-Time Uncertainty Relation
Entropic Energy-Time Uncertainty Relation
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DOI：
10.1103/physrevlett.122.100401
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发表时间：
2019-03-12
影响因子：
8.6
通讯作者：
Wilde, Mark M.
中科院分区：
文献类型：
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作者：
Coles, Patrick J.;Katariya, Vishal;Wilde, Mark M.
能量-时间不确定性在量子基础和量子技术中起着重要的作用，甚至量子力学的创始人也对它进行了讨论。然而，标准方法（例如，罗伯逊的不确定性关系）不适用于能量-时间不确定性，因为一般来说，没有厄米特算子与时间相关联。按照以前的方法，我们通过如何从量子时钟中读取时间来量化时间不确定性。然后，我们使用熵来量化时钟的各种时间状态的信息理论可重复性。我们的主要结果是一个熵的能量-时间的不确定性关系的一般时间无关的哈密顿量，离散时间和连续时间的情况下。我们的不确定性关系是强的，因为它允许量子记忆来帮助减少不确定性，这个公式使我们将其重新解释为不对称的相对熵的界限。由于熵的操作相关性，我们预计我们的不确定性关系将有信息处理的应用。
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Because of the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.