Revision 1

Superseded · first revision · record

Title: Do general measurements beat projective ones for Werner-state nonlocality?
Plain: 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: 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 $v_c$.
Settled by: A local model for all POVMs up to the projective threshold, or a POVM Bell inequality violated below it.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: The analogous steering question was settled in 2023: POVMs give no advantage and the threshold is $v = 1/2$ (arXiv:2309.09960).
Posed since: 2002