Watrous’s no-disentanglers conjecture; QMA versus QMA(2) relative to an oracle

Watrous’s conjecture asks whether approximate procedures that remove entanglement must use exponentially larger input dimension, a result that would separate the power of one versus two unentangled quantum proofs. The latest report claims this has been settled relative to a quantum oracle.

Known results

• Watrous (2008) conjectured that every $(\varepsilon,\delta)$-disentangler with fixed $\varepsilon,\delta<1$ requires $\dim H=2^{\Omega(\dim K)}$.
• Watrous (2008) proved the exact case $\varepsilon=\delta=0$: no finite-dimensional perfect disentangler exists when $\dim K\ge 2$.
• A 2024 preprint proved exponential bounds for strengthened disentanglers under $\varepsilon+\sqrt{\delta}<1$, but did not establish the stated oracle separation.

September 2, 2026 claimed oracle separation

A report dated September 2, 2026 says the authors of a new preprint prove a relative separation $\mathrm{QMA}\ne\mathrm{QMA}(2)$ and an exponential lower bound for $(\varepsilon,\delta)$-disentanglers whenever $\varepsilon+\delta<1$. This is a claimed resolution in the oracle setting, but it is not independently verified here and does not imply an unconditional separation.

Current status (as of September 2026): The claimed quantum-oracle separation and corresponding disentangler lower bound are reported but unverified; the unconditional question whether $\mathrm{QMA}=\mathrm{QMA}(2)$ remains open.