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A geometrical description of the universal \(1 \rightarrow 2\) asymmetric quantum cloning region

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Abstract

We consider the problem of determining the achievable region of the universal \(1 \rightarrow 2\) asymmetric quantum cloning problem. This concerns the quantum cloning of any quantum state to two approximate clones of different qualities. Measuring the cloning performance with the probabilities of the mixed clone states as the figure of merit, we show that the physical region is a union of ellipses in the plane. The study of these regions has consequences for the eavesdropping on quantum cryptography, and a wide variety of tasks. Equivalently, we characterize the region of quantum-state compatibility of two possibly different isotropic states, considering, for the first time, negative figures of merit.

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Acknowledgements

We would like to thank Satvik Singh for useful remarks about the paper. We are also thankful to the anonymous referees for their remarks which helped improve the quality of the presentation. This research was supported by the ANR project “ESQuisses” (ANR-20-CE47-0014-01). This research was supported by the ANR Program‘Investissements d’Avenir” with reference ANR-11-LABX-0040 trough the Labex CIMI. The research of C.P. has been supported by project “QTraj”(ANR-20-CE40-0024-01) of the French National Research Agency (ANR).

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, CNRS, UPS, Université de Toulouse (UMR 5152), 31062, Toulouse, Cedex 9, France

    Ion Nechita

  2. CNRS, UPS, Institut de Mathématiques, IMT, Université de Toulouse (UMR 5219), 31062, Toulouse, Cedex 9, France

    Clément Pellegrini & Denis Rochette

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  1. Ion Nechita
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  2. Clément Pellegrini
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  3. Denis Rochette
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Correspondence to Denis Rochette.

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Nechita, I., Pellegrini, C. & Rochette, D. A geometrical description of the universal \(1 \rightarrow 2\) asymmetric quantum cloning region. Quantum Inf Process 20, 333 (2021). https://doi.org/10.1007/s11128-021-03258-y

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