Narrow Results

If a set of local moves can transform every knot into a trivial knot, it is called a generalized unknotting operation. The author collects generalized unknotting operations and classify them up to local equivalence.

In this paper, we study the equivalence of quantum stabilizer codes via symplectic isometries of stabilizer codes. We define monomially and symplectically equivalent stabilizer codes and determine how different the two notions can be. Further, we show that monomial maps correspond to local Clifford operators. We relate the latter with the LU-LC Conjecture.

Linear entropy is widely used as a measure of operator entanglement of two-qubit gates. In this paper, we characterize the two-qubit gates of same linear entropy using the majorization criteria of the Schmidt coefficients of the gates. It is found that the gates with same linear entropy must have set of same Schmidt coefficients or set of different Schmidt coefficients which are not ordered according to the majorization relation.