Quantum money with nearly optimal error tolerance

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.

17 pages, 5 figures

References in corpus (7)

• Quantum cryptography: Public key distribution and coin tossing
• Quantum random number generation on a mobile phone
• Observation of quantum fingerprinting beating the classical limit
• Quantum Communication with Coherent States and Linear Optics
• Covert Quantum Communication
• Practical Quantum Retrieval Games
• Absolutely covert quantum communication

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• Semi-Device Independent Quantum Money
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• Practical quantum tokens without quantum memories and experimental tests
• Practical Quantum Appointment Scheduling
• Optimal quantum-programmable projective measurements with coherent states
• Characterization of Gram matrices of multimode coherent states
• Security Analysis of Ensemble-Based Quantum Token Protocol Under Advanced Attacks
• Noise-tolerant public-key quantum money from a classical oracle
• Benchmarking of Quantum Protocols