15 problems

Bell-pair superadditivity conjecture. There is an experiment on pairs of Bell singlets, of the $2\times4\times4$ type, more than twice as strong as CHSH, and involving joint measur…

CHSH optimality conjecture. The best experiment with the Bell singlet state is the CHSH experiment.

Let $1\leqslant m\leqslant N$ and let $N_1,\dots,N_m\geqslant 1$ be integers satisfying $N=N_1+\dots+N_m$. For the ground-state vectors of the open XXZ chain, define … The scalar p…

A flagged channel randomly selects one channel from a fixed ensemble and reports the selected channel along with the output state. A channel is strongly additive when its use toget…

Sanpera–Bruß–Lewenstein conjecture. All bound entangled states with positive partial transpose in $\mathbb{C}^3\otimes\mathbb{C}^3$ have Schmidt number $2$.

Logarithmic entanglement-scaling conjecture. The entanglement entropy of any such block, to leading order, scales as

Bravyi's Small Incremental Entangling conjecture. There is a universal constant $c$ such that, for all ancilla dimensions, all states $|\Psi\rangle$, and all such Hamiltonians,

Let $d\geqslant 2$ and let $\pi_{d,s}$ denote the probability that a random state on $\mathbf{C}^d\otimes\mathbf{C}^d$ with distribution $\mu_{d^2,s}$ is separable. Monotonicity co…

Generalized Distillability Conjecture. All generalized critical Werner states $\rho_{(d_1,\ldots,d_m)}^W$, $m\geq1$, are $1$-indistillable.

Let $\rho$ be a bipartite quantum state. It is NPT if its partial transpose is not positive semidefinite, and indistillable if no tensor power of $\rho$ is $1$-distillable. Distill…

Generic determinant conjecture for the Werner-state matrix $H$. $D(X,Y)\ne0$ for generic $(X,Y)$ and $d\ge3$.

Positivity conjecture for the Werner-state matrix $H$. The matrix $H(X,Y)$ is positive semidefinite for all $X,Y\in M_d$.

2-distillability conjecture for Werner states. None of the Werner states $\rho_W(t)$, $t\in(1/d,1/2]$, is $2$-distillable.

Werner-state nondistillability conjecture. None of the Werner states $\rho_W(t)$, $t\in(1/d,1/2]$, is distillable.

NPT bound-entanglement conjecture. There exist bipartite NPT states which are not distillable.