Sub-linear resource scaling of quantum resources versus number of verifications

Reduce the quantum resource consumption of the publicly verifiable quantum money scheme based on one-time memories and collision-resistant hash functions from linear dependence on the maximum number of verifications N to sub-linear growth, while preserving the requirement of only minimal single-qubit quantum capabilities.

Background

In the presented construction, each verification consumes a fixed number of OTMs via cut-and-choose, so supporting N independent verifications requires quantum resources that scale linearly with N. This limits the lifetime of a banknote and increases preparation and storage overhead proportionally to N.

The authors highlight the challenge of achieving improved (sub-linear) scaling in the number of required OTM states while maintaining the minimal quantum capabilities assumption (preparing, transmitting, and measuring single-qubit states in conjugate bases), which is crucial for near-term practicality.