5 problems

Near-half-system entropy-difference conjecture. The difference is also $\Omega(1)$ if

Let $\Delta S_1$ denote the Page correction to the von Neumann entanglement entropy of a subsystem in a constrained system, and let Page's result be the corresponding correction fo…

Relative entropy of entanglement conjecture. For

Let $\mathcal{S}_N$ be the symmetric subspace of $N$ qubits, let $\mu(\mathcal{S}_N)$ denote its unitarily invariant probability measure, and let…

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…