More is Less:Optimal Security for Haar Quantum Money and More
Abstract
Quantum cryptography leverages unclonability to enable a wide range of cryptographic applications that are impossible classically, such as digital currency protected against counterfeiting by quantum mechanics. Security requires that no efficient user can produce even one additional valid banknote beyond those already in their possession. However, existing security bounds weaken as the number of banknotes available to a user increases. In this paper, we study a construction of quantum money whose asymptotic query security does not deteriorate as long as the number of banknotes available to a user remains below the scale required for state tomography. In particular, we show that the construction based on an n-qubit Haar-random state and a reflection oracle achieves optimal query security: unless a user holds Ω(2n) banknotes, their existing banknotes cannot asymptotically speed up counterfeiting --- their best possible attack is the same as if they do not have any banknotes. To establish this result, we develop a framework based on the compressed-oracle technique for defining and analyzing progress measures for quantum tasks such as Haar state cloning. Furthermore, we prove a tight lower bound for generating r additional copies, give a matching attack, and apply our results to quantum copy-protection.
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BibTeX
@misc{hao2026more,
title = {{More is Less:Optimal Security for Haar Quantum Money and More}},
author = {Zihan Hao and Xingjian Li and Qipeng Liu and Wei Zhan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40184},
eprint = {2609.40184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40184},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - More is Less:Optimal Security for Haar Quantum Money and More
AU - Zihan Hao
AU - Xingjian Li
AU - Qipeng Liu
AU - Wei Zhan
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40184
UR - https://arxiv.org/abs/2609.40184
AB - Quantum cryptography leverages unclonability to enable a wide range of cryptographic applications that are impossible classically, such as digital currency protected against counterfeiting by quantum mechanics. Security requires that no efficient user can produce even one additional valid banknote beyond those already in their possession. However, existing security bounds weaken as the number of banknotes available to a user increases. In this paper, we study a construction of quantum money whose asymptotic query security does not deteriorate as long as the number of banknotes available to a user remains below the scale required for state tomography. In particular, we show that the construction based on an n-qubit Haar-random state and a reflection oracle achieves optimal query security: unless a user holds Ω(2^n) banknotes, their existing banknotes cannot asymptotically speed up counterfeiting --- their best possible attack is the same as if they do not have any banknotes. To establish this result, we develop a framework based on the compressed-oracle technique for defining and analyzing progress measures for quantum tasks such as Haar state cloning. Furthermore, we prove a tight lower bound for generating r additional copies, give a matching attack, and apply our results to quantum copy-protection.
ER -