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Complementary relation between quantum entanglement and entropic uncertainty
Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2020-12-18 , DOI: 10.1088/1572-9494/abc46f
Yun Cao 1 , Dong Wang 1, 2 , Xiao-Gang Fan 1 , Fei Ming 1 , Zhang-Yin Wang 1 , Liu Ye 1
Affiliation  

Quantum entanglement is regarded as one of the core concepts, which is used to describe the non-classical correlation between subsystems, and entropic uncertainty relation plays a vital role in quantum precision measurement. It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states. An interesting question is naturally raised: is there any intrinsic correlation between the entropic uncertainty relation and quantum entanglement? Or if the relation can be applied to estimate the entanglement. In this work, we focus on exploring the complementary relation between quantum entanglement and the entropic uncertainty relation. The results show that there exists an inequality relation between both of them for an arbitrary two-qubit system, and specifically the larger uncertainty will induce the weaker entanglement of the probed system, and vice versa. Besides, we use randomly generated states as illustrations to verify our results. Therefore, we claim that our observations might offer and support the validity of using the entropy uncertainty relation to estimate quantum entanglement.



中文翻译:

量子纠缠与熵不确定性之间的互补关系

量子纠缠被视为核心概念之一,用于描述子系统之间的非经典相关性,熵不确定性关系在量子精度测量中起着至关重要的作用。众所周知,对于任意纯态,形成的纠缠可以通过子系统的冯·诺依曼熵表示。自然会提出一个有趣的问题:熵不确定性关系和量子纠缠之间是否有内在联系?或者该关系是否可以应用于估计纠缠。在这项工作中,我们专注于探索量子纠缠与熵不确定性关系之间的互补关系。结果表明,对于一个任意的二量子位系统,两者之间存在不等式关系,特别是较大的不确定性将导致所探测系统的纠缠较弱,反之亦然。此外,我们使用随机生成的状态作为例证来验证我们的结果。因此,我们声称我们的观察可能提供并支持使用熵不确定性关系来估计量子纠缠的有效性。

更新日期:2020-12-18
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