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Uncertainty relations based on mutually unbiased measurements

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Abstract

We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by \(d+1\) MUMs on any density operator \(\rho \) in \({\mathbb {C}}^{d}\), both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of Rényi and Tsallis entropies.

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Acknowledgments

This work is supported by the NSFC under number 11275131.

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Correspondence to Bin Chen.

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Chen, B., Fei, SM. Uncertainty relations based on mutually unbiased measurements. Quantum Inf Process 14, 2227–2238 (2015). https://doi.org/10.1007/s11128-015-0949-5

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