E. Jonckheere, S. G. Schirmer, F.C. Langbein. Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers. Submitted 2016. [arXiv:1612.02784] [PDF]
Selective information transfer in spin ring networks by landscape shaping control has the property that the error 1−prob, where prob is the transfer success probability, and the sensitivity of the probability to spin coupling errors are “positively correlated,” meaning that both are statistically increasing across a family of controllers of increasing error. Here, we examine the rank correlation between the error and another measure of performance-the logarithmic sensitivity-used in robust control to formulate the fundamental limitations. Contrary to error versus sensitivity, the error versus logarithmic sensitivity correlation is less obvious, because its weaker trend is made difficult to detect by the noisy behavior of the logarithmic sensitivity across controllers of increasing error numerically optimized in a challenging landscape. This results in the Kendall tau test for rank correlation between the error and the log sensitivity to be pessimistic with poor confidence. 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 problem and hence singles out cases of anti-classical behavior of “positive correlation” between the error and the logarithmic sensitivity.
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