Entropic uncertainty from effective anticommutators

Publication Type:
Journal Article
Citation:
Physical Review A - Atomic, Molecular, and Optical Physics, 2014, 90 (1)
Issue Date:
2014-07-22
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We investigate entropic uncertainty relations for two or more binary measurements, for example, spin-12 or polarization measurements. We argue that the effective anticommutators of these measurements, i.e., the anticommutators evaluated on the state prior to measuring, are an expedient measure of measurement incompatibility. Based on the knowledge of pairwise effective anticommutators we derive a class of entropic uncertainty relations in terms of conditional Rényi entropies. Our uncertainty relations are formulated in terms of effective measures of incompatibility, which can be certified in a device-independent fashion. Consequently, we discuss potential applications of our findings to device-independent quantum cryptography. Moreover, to investigate the tightness of our analysis we consider the simplest (and very well studied) scenario of two measurements on a qubit. We find that our results outperform the celebrated bound due to Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)PRLTAO0031-900710.1103/PhysRevLett.60.1103] and provide an analytical expression for the minimum uncertainty which also outperforms some recent bounds based on majorization. © 2014 American Physical Society.
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