New Kochen-Specker Sets in Four Dimensions

摘要

We show that all possible 388 4-dim Kochen-Specker (KS) (vector) sets (ofyes-no questions) with 18 through 23 vectors and 844 sets with 24 vectors allwith component values from \{-1,0,1\} can be obtained by stripping vectors offa single system provided by Peres 20 years ago. In addition to them, we havefound a number of other KS sets with 22 through 24 vectors. We present thealgorithms we used and features we found, such as, for instance, that Peres'24-24 KS set has altogether six critical KS subsets.