17 problems

Multiseparability conjecture. Any MS system should separate in multiple coordinate systems.

Let $G$ be a closed orientable hyperbolic surface group, let $H$ be a finitely generated subgroup of infinite index in $G$, and let $\{\gamma_1,\ldots,\gamma_n\}$ be any finite set…

Teukolsky's separability conjecture. Separability should be preserved, or granted, under coordinate transformations of the displayed form.

Separability conjecture. The space $X$ is separable.

Let $M_A$ be a matrix algebra, and let $\varrho_1,\varrho_2\in M_A\otimes M_A$ be states. Let $\varrho_1\square\varrho_2\in M_A\otimes(M_A\otimes M_A)$ denote their block Schur pro…

S-separability conjecture. A completely symmetric state is separable if and only if it is S-separable.

Characterization problem. Is $G\in\mathfrak{S}$ if and only if $G$ contains a compact separable subgroup $K$ such that the quotient space $G/K$ is countable?

Let a qubit–qubit or qubit–qutrit state have block form … where $D=D_{1}+D_{2}$ is the reduced state on a single-qubit subsystem, and let $r$ denote the Bloch radius of $D$. Milz–S…

Goodman–Goodman conjecture. For every convex body $\mathbf K$ in $\mathbb R^d$ and every non-separable family $\mathcal K$ as above, $\lambda(\mathcal K)\leq 1$ for all $d\geq 2$ a…

Braunstein's conjecture. The state $\rho_l(G)$ is separable in any dimension if and only if $G$ and $G'$ have the same degree sequence.

Let $\varrho_{\mathrm{SDS}}$ denote the set of separable diagonal-symmetric states, and let $\varrho_{\mathrm{GDS}}$ denote the set of generalized Dicke-symmetric states. Let…

Let $\rho$ be a strong positive partial transpose (SPPT) state, namely, a PPT state whose PPT properties are ensured by the canonical construction using Cholesky decomposition. A q…

A projective Banach lattice is a Banach lattice with the projective lifting property, and a topological order unit is an element whose principal order ideal is dense in the lattice…

The witness form of the SPA conjecture. Let $W$ be an optimal entanglement witness with $\operatorname{Tr}(W)=1$. Then $\tilde{W}(p_*)$ defines a separable state.

Characterization and cardinal-invariant conjecture. begin{enumerate} item A compact space $X$ is D-separable if and only if $X$ has a $\sigma$-disjoint $\pi$-base. item For every c…

For each positive integer $n$, let $g(n)$ be the least threshold such that every $k$-latin square of order $n$ is separable whenever $k\geq g(n)$. The paper proves that such a fini…

Let $G$ be a group hyperbolic relative to the peripheral system $\mathcal{P}=\{P_1,\ldots,P_n\}$. Suppose that hyperbolic groups are residually finite, and that each $P_i$ is finit…