Conditional entropic uncertainty and quantum correlations

Abstract

Uncertainty relations reflect the inevitability inbuilt within the quantum framework, preventing prediction of precise outcomes for non-commuting observables. Maassen–Uffinkentropic uncertainty relation (Maassen and Uffink, 1988) captures the trade-off in the spread of the outcomes of a pair of non-commuting observables. Entropic uncertainty relation in the presence of quantum memory (Berta et al., 2010) brought about a fascinating twist by showing that quantum side information, enabled via entanglement, helps in beating the uncertainty of non-commuting observables. In this paper we investigate conditional entropic uncertainty relation and bring out an interplay between non-classical correlations – arising from sequential measurements in a single quantum system – and the entropic uncertainty bound. Our main result is formulated as a theorem, which establishes that if correlations between outcomes of sequential measurements are classical, the uncertainty bound on the sum of conditional entropies of non-commuting observables does not get reduced below the Maassen–Uffink bound.