Do general measurements beat projective ones for Werner-state nonlocality?
In plain words
Measurements can be generalized beyond simple projections by using helper systems. For Werner states it is unknown whether such generalized measurements reveal nonlocality at higher noise than projective ones.
Precise statement
Let $v_c^{\mathrm{POVM}}$ be the critical visibility of $\rho_W(v)$ under arbitrary local POVMs. Known: rho_W(v) is local for all POVMs when $v \le 1/2$ (Zhang and Chitambar, arXiv:2309.09960) and for projective measurements when $v \le 0.6875$. Determine whether $v_c^{\mathrm{POVM}}$ equals the projective threshold $v_c$.
What would settle it
A local model for all POVMs up to the projective threshold, or a POVM Bell inequality violated below it.
Status in the literature
The analogous steering question was settled in 2023: POVMs give no advantage and the threshold is $v = 1/2$ (arXiv:2309.09960).