  Selective information transfer in spin ring networks by energy landscape
shaping control has the property that the error 1-prob, where prob is the
transfer success probability, and the sensitivity of the error to spin coupling
uncertainties are statistically increasing across a family of controllers of
increasing error. The need for a statistical Hypothesis Testing of a concordant
trend is made necessary by the noisy behavior of the sensitivity versus the
error as a consequence of the optimization of the controllers in a challenging
error landscape. Here, we examine the concordant trend between the error and
another measure of performance - the logarithmic sensitivity - used in robust
control to formulate a well known fundamental limitation. Contrary to error
versus sensitivity, the error versus logarithmic sensitivity trend is less
obvious, because of the amplification of the noise due to the logarithmic
normalization. This results in the Kendall {\tau} test for rank correlation
between the error and the log sensitivity to be somewhat pessimistic with
marginal significance level. Here it is shown that the Jonckheere-Terpstra
test, because it tests the Alternative Hypothesis of an ordering of the medians
of some groups of log sensitivity data, alleviates this statistical problem.
This identifies cases of concordant trend between the error and the logarithmic
sensitivity, a highly anti-classical features that goes against the well know
sensitivity versus complementary sensitivity limitation.
