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Limitations imposed by complementarity

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Abstract

Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible observables. For two-level systems, it is shown that any preparation violating complementarity enables the preparation of a non-signalling box violating Tsirelson’s bound. Moreover, these “beyond-quantum” objects could be used to distinguish a plethora of non-orthogonal quantum states and hence enable improved cloning protocols. For higher-dimensional systems the main ideas are sketched.

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  1. Minus the null measure set constituted by the states \(\rho ({\hat{\mathbf {n}}}_+)\) on the equatorial circle of the Bloch sphere.

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Acknowledgements

We are thankfull to C. Brukner, E. F. Galvão, M. F. Cornelio, A. V. Saa, R. A. Mosna and P. E. M. F. Mendonça for comments and suggestions in previous versions of this work and to P. Blasiak, C. Budroni and M. Kleinmman for comments and discussions that helped to improve the ideas and the overall presentation of this work. We are thankfull as well to M. Huber for important suggestions regarding higher-dimensional systems. This work is part of the institutional project 346/2017 from the Universidade Federal de Mato Grosso and was supported by CAPES, by the EU (Marie Curie CIG 293993/ENFOQI), the BMBF (Chist-Era Project QUASAR), the FQXi Fund (Silicon Valley Community Foundation), and the DFG. MCO acknowledges support from CNPq/FAPESP through the Instituto Nacional de Ciência e Tecnologia em Informação Quântica (INCT-IQ) and FAPESP through the Research Center in Optics and Photonics (CePOF).

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Steinhoff, F.E.S., de Oliveira, M.C. Limitations imposed by complementarity. Quantum Inf Process 19, 358 (2020). https://doi.org/10.1007/s11128-020-02869-1

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