Quantum-resource separation for random-function f-BB84 schemes

Determine whether the ancilla-size lower bounds known for random-function f-BB84 schemes establish a separation between the quantum resources required by honest and dishonest players, particularly when classical memory used by a physical attacker may be counted as quantum ancilla in the purified model.

Background

The paper discusses prior lower bounds for random-function f-BB84 schemes that concern the quantum ancilla size of an attacker, and notes that these bounds are obtained in a purified model. Because such a model may treat an attacker's classical memory as quantum ancilla, the authors leave unresolved whether the results demonstrate a genuine separation in the quantum resources required by honest and dishonest participants.

References

This purified model may be counting classical memory used by a physical attacker as quantum ancilla, so it is not clear if this establishes a separation in the quantum resources needed by an honest or dishonest player.

— Quantum gate lower bounds for loss-tolerant position verification  (2608.16495 - May et al., 17 Aug 2026) in Section 1, subsection “Prior work”

In the discrete-time model, we provide a family of QPV protocols, such that for every polynomial $p()$ there is a protocol in the family that achieves that resource gap $p()$. However, this is not tight, and in particular, does not match the impossibility result of Buhrman et al. only rules out arbitrary (exponential) resource gap. This leaves open the question of constructing a single QPV protocol that achieves an arbitrary polynomial resource gap, or even a fixed exponential resource gap.

— Breaking the Bounded Entanglement Barrier for Quantum Position Verification  (2609.39234 - Behera et al., 30 Sep 2026) in Section 1, subsection “Open Questions” (Section 1.4)