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Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement

Nature Physics volume 7, pages 757–761 (2011)Cite this article

Abstract

Heisenberg’s uncertainty principle1 provides a fundamental limitation on the ability of an observer holding classical information to predict the outcome when one of two measurements is performed on a quantum system. However, an observer with access to a particle (stored in a quantum memory) which is entangled with the system generally has a reduced uncertainty: indeed, if the particle and system are maximally entangled, the observer can perfectly predict the outcome of whichever measurement is chosen. This effect has recently been quantified2 in a new entropic uncertainty relation. Here we experimentally investigate this relation, showing its effectiveness as an efficient entanglement witness. We use entangled photon pairs, an optical delay line serving as a simple quantum memory and fast, active feed-forward. Our results quantitatively agree with the new uncertainty relation. Our technique acts as a witness for almost all entangled states in our experiment as we obtain lower uncertainties than would be possible without the entangled particle3,4,5.

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Figure 1: Schematic of the experiment.
Figure 2: Experimental results.
Figure 3: Uncertainties for other experimental settings.

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Acknowledgements

We thank M. Piani for valuable discussions and the Ontario Ministry of Research and Innovation ERA, QuantumWorks, NSERC, OCE, Industry Canada and CFI for financial support. R.P. acknowledges support by MRI and the Austrian Science Fund (FWF).

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Authors and Affiliations

  1. Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

    Robert Prevedel, Deny R. Hamel, Kent Fisher & Kevin J. Resch

  2. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

    Roger Colbeck

Authors
  1. Robert Prevedel
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  2. Deny R. Hamel
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  3. Roger Colbeck
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  4. Kent Fisher
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  5. Kevin J. Resch
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Contributions

K.J.R., R.P. and R.C. designed the experiment. R.P., D.R.H. and K.F. performed the experiment. R.C. provided theoretical support. R.P. analysed the data. R.P. and R.C. wrote the paper. All authors discussed and contributed to the final version of the manuscript.

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Correspondence to Robert Prevedel.

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The authors declare no competing financial interests.

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Prevedel, R., Hamel, D., Colbeck, R. et al. Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nature Phys 7, 757–761 (2011). https://doi.org/10.1038/nphys2048

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