6 problems

A unitary operator is represented by a unitary four-diagonal matrix when its matrix in an orthonormal basis is unitary and four-diagonal, meaning that its entries vanish outside th…

UBB conjecture. There always exists a pair of maximally entangled states, $\ket{\Psi_1}$ and $\ket{\Psi_2}$, such that

Let $U$ and $U'$ be bipartite unitary operators on $\mathcal{H}_3\otimes\mathcal{H}_3$. They are local unitarily equivalent if there exist single-qutrit unitary gates…

Consider pairwise commuting unitary semiclassical operators $U_1(\hbar), \ldots, U_d(\hbar)$ with joint principal symbol $F=(f_0^1,\ldots,f_0^d)$, and assume that $F(M)$ is closed.…

Let $U_1$ and $U_2$ be unitary operators whose spectral measures are singular with respect to Lebesgue measure, let $X$ be an operator, and define the commutator … Assume that $K$…

Let ${\cal P}$ be the family of polynomials considered in the paper, and let the decomposition described in Theorem A be the decomposition into closed $U$-invariant subspaces satis…