Quantum money with nearly optimal error tolerance

TL;DR

This paper introduces quantum money schemes with classical verification that are highly noise-tolerant, nearly reaching the theoretical maximum of 25%, and are practical for implementation with current technology.

Contribution

The authors develop nearly optimal noise-tolerant quantum money schemes based on hidden matching games, with efficient verification and reusability, using semi-definite programming for security proof.

Findings

Noise tolerance up to 23%, conjectured to reach 25% asymptotically.

Verification involves only a constant number of states, enabling smaller coins.

Coin reusability grows linearly with coin size, which is optimal.

Abstract

We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23%, which we conjecture reaches 25% asymptotically as the dimension of the underlying hidden matching states is increased. Furthermore, we prove that 25% is the maximum tolerable noise for a wide class of quantum money schemes with classical verification, meaning our schemes are almost optimally noise tolerant. We use methods in semi-definite programming to prove security in a substantially different manner to previous proposals, leading to two main advantages: first, coin verification involves only a constant number of states (with respect to coin size), thereby allowing for smaller coins; second, the re-usability of coins within our scheme grows linearly with the size of the coin, which is known to be optimal. Lastly, we suggest methods by which the coins in our protocol could be implemented using weak coherent states and verified using existing experimental techniques, even in the presence of detector inefficiencies.