Complementary relation between quantum entanglement and entropic uncertainty |
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Authors: | Yun Cao Dong Wang Xiao-Gang Fan Fei Ming Zhang-Yin Wang Liu Ye |
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Institution: | 1.School of Physics & Material Science, Anhui University, Hefei 230601, China;2.CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China |
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Abstract: | 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. |
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Keywords: | uncertainty relation entanglement of formation concurrence |
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