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Universality and Optimality in the Information–Disturbance Tradeoff

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Abstract

We investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann measurement, then the optimal tradeoff can always be achieved within a two-parameter family of quantum devices that is independent of the chosen distance measures. This form of almost universal optimality holds under mild assumptions on the distance measures such as convexity and basis independence, which are satisfied for all the usual cases that are based on norms, transport cost functions, relative entropies, fidelities, etc., for both worst-case and average-case analyses. We analyze the case of the cb-norm (or diamond norm) more generally for which we show dimension independence of the derived optimal tradeoff for general von Neumann measurements. A SDP solution is provided for general POVMs and shown to exist for arbitrary convex semialgebraic distance measures.

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Acknowledgements

The authors would like to thank Teiko Heinosaari for many useful comments. AKHs work is supported by the Elite Network of Bavaria through the PhD program of excellence Exploring Quantum Matter. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Munich, Munich, Germany

    Anna-Lena K. Hashagen & Michael M. Wolf

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, USA

    Michael M. Wolf

Authors
  1. Anna-Lena K. Hashagen
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  2. Michael M. Wolf
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Correspondence to Anna-Lena K. Hashagen.

Additional information

Communicated by David Pérez-García.

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Hashagen, AL.K., Wolf, M.M. Universality and Optimality in the Information–Disturbance Tradeoff. Ann. Henri Poincaré 20, 219–258 (2019). https://doi.org/10.1007/s00023-018-0724-0

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