Quantum / CONCEPT
The X-state conditional entropy f_1 need not be weakly unimodal
Yurischev (arXiv:1702.03728, Quantum Inf. Process. 16, 249) writes the conditional entropy of a two-qubit X state through the function f_1 of Eq. (A1) on [0, 1] and supposes that it is weakly unimodal for every choice of the parameters p_1, ..., p_5 with nonnegative Shannon arguments. It is not: for p = (-2466, -1107, 187, -163, 1138)/2500 one has f_1(0) > f_1(27/50) < f_1(177/200) > f_1(1).
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A non-unimodal conditional entropy
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