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Experimental investigation of the entanglement-assisted entropic uncertainty principle

Nature Physics volume 7, pages 752–756 (2011)Cite this article

Abstract

The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in terms of entropy has been extended to the case involving quantum entanglement1. With previously obtained quantum information for the particle of interest, the outcomes of both non-commuting observables can be predicted precisely, which greatly generalizes the uncertainty relation. Here, we experimentally investigated the entanglement-assisted entropic uncertainty principle for an entirely optical set-up. The uncertainty is shown to be near zero in the presence of quasi-maximal entanglement. The new uncertainty relation is further used to witness entanglement. The verified entropic uncertainty relation provides an intriguing perspective in that it implies the uncertainty principle is not only observable-dependent but is also observer-dependent2.

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Figure 1: Experimental setup.
Figure 2: Experimental results for the conditional entropies with the input state ρ1.
Figure 3: Experimental results for the entanglement witness using the input state of ρ1.
Figure 4: Experimental results for the density matrix χ of the spin-echo based quantum memory and the entropies as a function of the angle θ.

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Acknowledgements

This work was supported by the National Basic Research Program of China (Grants No. 2011CB921200), National Natural Science Foundation of China (Grant Nos 11004185, 60921091, 10874162), and the China Postdoctoral Science Foundation (Grant No. 20100470836). The CQT is funded by the Singapore MoE and the NRF as part of the Research Centres of Excellence programme.

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Author notes

  1. Chuan-Feng Li and Jin-Shi Xu: These authors contributed equally to this work

Authors and Affiliations

  1. Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China

    Chuan-Feng Li, Jin-Shi Xu, Xiao-Ye Xu & Guang-Can Guo

  2. Center for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542, Singapore

    Ke Li

Authors
  1. Chuan-Feng Li
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  2. Jin-Shi Xu
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  3. Xiao-Ye Xu
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  4. Ke Li
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Contributions

C-F.L. and J-S.X. designed the experiment. C-F.L. supervised the project. J-S.X. and X-Y.X. performed the experiment. J-S.X. analysed the theoretical prediction and experimental data. K.L. and G-C.G. contributed to the theoretical analysis. X-Y.X. drew the sketch of the experimental setup. J-S.X. wrote the paper. All authors commented on the manuscript.

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Correspondence to Chuan-Feng Li.

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The authors declare no competing financial interests.

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Li, CF., Xu, JS., Xu, XY. et al. Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nature Phys 7, 752–756 (2011). https://doi.org/10.1038/nphys2047

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