Obtain a general closed form for the jamming-game quantum value

Determine a general closed-form expression for the quantum value of the $(n,k)$ jamming game, in which two parties receive private safe subsets of $n$ frequency bands and must independently select a common usable band.

Background

The jamming game has an exact classical value given by a combinatorial formula. Its quantum value measures the best achievable probability that the parties select the same safe frequency despite receiving different private safe sets.

The paper applies BGD to obtain feasible quantum strategies and numerical lower bounds for large instances, but does not provide a general formula for the quantum optimum. A closed form would clarify the scaling of quantum advantage across the parameters nn and kk.

References

while the quantum value has no general closed form.

— Efficiently Optimizing the Quantum Value of Bell Inequalities using Batched Gradient Descent  (2610.01699 - Xu et al., 1 Oct 2026) in Section 7, subsection “The $(n,k)$ jamming game $(2,\binom{n}{n-k},n-k)$”