We introduce a new quantum Gromov-Hausdorff distance between C∗-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel’s quantum distance. We show that this new quantum distance has properties analogous to the basic properties of the classical Gromov-Hausdorff distance, and we give criteria for when a parame...

The k-ellipse is the plane algebraic curve consisting of all points whose sum of distances from k given points is a fixed number. The polynomial equation defining the k-ellipse has degree 2k if k is odd and degree 2k− ` k k/2 ́ if k is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted k-ellipses and k-...

It is shown that a Boolean combining function f(x) of n variables is mth-order correlation immune if and only if its Walsh transform F(w) vanishes for all w with Hamming weights between 1 and m, inclusive. This result is used to extend slightly Siegenthaler’s characterization of the algebraic normal form of correlation-immune combining functions.