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Weak quantum discord

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Abstract

Originally introduced as the difference between two possible forms of quantum mutual information, quantum discord has posteriorly been shown to admit a formulation according to which it measures a distance between the state under scrutiny and the closest projectively measured (non-discordant) state. Recently, it has been shown that quantum discord results in higher values when projective measurements are substituted by weak measurements. This sounds paradoxical since weaker measurements should imply weaker disturbance and, thus, a smaller distance. In this work, we solve this puzzle by presenting a quantifier and an underlying interpretation for what we call weak quantum discord. As a by-product, we introduce the notion of symmetrical weak quantum discord.

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Notes

  1. Of course, the WQD also vanishes for \(\varepsilon \rightarrow 0\), but this trivial limit is not included in the statement of Theorem 1.

  2. Of course, the SyWQD will also vanishes for \((\varepsilon ',\varepsilon )\rightarrow (0,0)\).

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Acknowledgements

P. R. Dieguez and R. M. Angelo, respectively, acknowledge financial support from the Brazilian Agencies CAPES and CNPq. This work was partially supported by the National Institute for Science and Technology of Quantum Information (INCT-IQ/CNPq, Brazil).

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Authors and Affiliations

  1. Department of Physics, Federal University of Paraná, P.O. Box 19044, Curitiba, Paraná, 81531-980, Brazil

    P. R. Dieguez & R. M. Angelo

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  1. P. R. Dieguez
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  2. R. M. Angelo
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Correspondence to R. M. Angelo.

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Dieguez, P.R., Angelo, R.M. Weak quantum discord. Quantum Inf Process 17, 194 (2018). https://doi.org/10.1007/s11128-018-1963-1

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