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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Uncertainty Equality with Quantum Memory and Its Experimental Verification

Hengyan Wang, Zhi-Hao Ma, Shengjun Wu, Wenqiang Zheng, Zhu Cao, Zhi-Hua Chen, Zhaokai Li, Shao-Ming Fei, Xinhua Peng, Jiangfeng Du and Vlatko Vedral


As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. A natural and fundamental question is whether an equality exists for the uncertainty principle. Here we derive an entropic uncertainty equality relation for a bipartite system consisting of a quantum system and a coupled quantum memory, based on the information measure introduced by Brukner and Zeilinger in [Phys. Rev. Lett. 83, 3354 (1999)]. The equality indicates that the sum of measurement uncertainties over a complete set of mutually unbiased bases on a subsystem is equal to a total, fixed uncertainty determined by the initial bipartite state.

For the special case where the system and the memory are the maximally entangled, all of the uncertainties related to each mutually unbiased base measurement are zero, which is substantially different from the uncertainty inequality relation. The results are meaningful for fundamental reasons and give rise to operational applications such as in quantum random number generation and quantum guessing games.

Moreover, we experimentally verify the measurement uncertainty relation in the presence of quantum memory on a 5-qubit spin system by directly measuring the corresponding quantum mechanical observables, rather than quantum state tomography in all the previous experiments of testing entropic uncertainty relations.


Related publications

2019 Journal Open Access
Hengyan Wang, Zhi-Hao Ma, Shengjun Wu, Wenqiang Zheng, Zhu Cao, Zhi-Hua Chen, Zhaokai Li, Shao-Ming Fei, Xinhua Peng, Vlatko Vedral and Jiangfeng Du

Uncertainty equality with quantum memory and its experimental verification

In: npj Quantum information, 5 (2019), p. 39