Sharp comparison of probabilistic retrieval and exact virtual programming

Determine whether probabilistic retrieval and exact virtual programming can be compared sharply under a common memory constraint.

Background

The paper compares exact virtual programming, in which physical channels are sampled and measurement outcomes are classically reweighted, with probabilistic physical retrieval. It derives a one-way bound converting uniform-success probabilistic retrieval with success probability q into an exact virtual retriever with overhead at most 2/q−1.

The paper explicitly notes that the converse comparison does not follow and that success probabilities optimized over different program memories cannot directly be inserted into the same-Choi bound. The open question is therefore to establish a sharp, operationally fair comparison when both approaches are evaluated using a common memory constraint.