The no-disentanglers conjecture asserts that a quantum channel cannot efficiently parametrize all separable bipartite states while ensuring
that all its outputs are nearly separable. In the formulation discussed by Bostanci
et al. (2026), an 
-disentangler has every output within trace
distance 
of a separable state, and every separable state within
trace distance 
of some output.
The conjecture predicts an exponential input-size requirement as a function of the number of output qubits. The two approximation conditions are essential. A channel that always prepares one fixed product state meets the first condition but cannot approximate all separable states.
Bostanci et al. (2026) proved the exponential lower bound whenever 
, using their quantum oracle separation of
QMA(2) from QMA. The construction was co-developed with GPT-5.6
Sol and checked by the authors. Independent external verification had not been reported
as of Sep. 7, 2026.
