5 problems

For a multipartite quantum state, its local unitary orbit is the orbit under the action of the local unitary group. Zhang–Xie conjecture. The local unitary orbit of an arbitrary mu…

Let $n\geqslant3$, let $d\geqslant2$, and let $(\psi_1,\ldots,\psi_n)$ be an $n$-tuple of pure states in $\mathbb{C}^d$. Write $4\psi_k=|\psi_k\rangle\langle\psi_k|4$ and choose pu…

Polar-boundary conjecture. For $n\geqslant3$,

For $n greater than or equal to3$, let $4mathcal{B}n4$ denote the set of $n$th-order Bargmann invariants, $4mathcal{B}{n,2}4$ the corresponding qubit set, and…

Let $4n4$th-order Bargmann invariants be the unitary invariants formed from cyclic products of inner products of $n$ pure states, and let their attainable sets have boundaries desc…