Codekets

Abstract

To every binary linear [n,k]-code C we associate a quantum state ("codeket") belonging to the n-th tensor power of the 2-dimensional complex Hilbert space associated to the spin 1/2 particle. We completely characterize the expectation values of the products of x-, y- or z- spins measured in the state we define, for each of the particles in a chosen subset. This establishes an interesting relationship with the dual code. We also address the case of nonlinear codes, and derive both a bound satisfied by the expectations of spin products, as well as a nice algebraic identity.