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Optimal Counterfeiting Attacks and Generalizations for Wiesner’s Quantum Money

Molina, Abel and Vidick, Thomas and Watrous, John (2013) Optimal Counterfeiting Attacks and Generalizations for Wiesner’s Quantum Money. In: Theory of Quantum Computation, Communication, and Cryptography. Lecture Notes in Computer Science. No.7582. Springer , Berlin, pp. 45-64. ISBN 978-3-642-35655-1.

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We present an analysis of Wiesner’s quantum money scheme, as well as some natural generalizations of it, based on semidefinite programming. For Wiesner’s original scheme, it is determined that the optimal probability for a counterfeiter to create two copies of a bank note from one, where both copies pass the bank’s test for validity, is (3/4)^n for n being the number of qubits used for each note. Generalizations in which other ensembles of states are substituted for the one considered by Wiesner are also discussed, including a scheme recently proposed by Pastawski, Yao, Jiang, Lukin, and Cirac, as well as schemes based on higher dimensional quantum systems. In addition, we introduce a variant of Wiesner’s quantum money in which the verification protocol for bank notes involves only classical communication with the bank. We show that the optimal probability with which a counterfeiter can succeed in two independent verification attempts, given access to a single valid n-qubit bank note, is (3/4+√2/8)^n. We also analyze extensions of this variant to higher-dimensional schemes.

Item Type:Book Section
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Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2013 Springer-Verlag Berlin Heidelberg. Supported by NSERC, MITACS, a Mike and Ophelia Lazaridis Graduate Fellowship, and a David R. Cheriton Graduate Scholarship. Supported by the National Science Foundation under Grant No. 0844626. Supported by NSERC, CIFAR, and MITACS. We thank Scott Aaronson for his question [11] on Theoretical Physics Stack Exchange that originated the results in this paper as an answer, and Peter Shor for pointing out the connection between the channel representing an optimal attack on Wiesner’s quantum money, and the optimal cloners studied in [8] and [9]. JW thanks Debbie Leung and Joseph Emerson for helpful discussions. AM thanks Michael Grant and Stephen Boyd for their creation of the CVX software.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Mike and Ophelia Lazaridis Graduate FellowshipUNSPECIFIED
David R. Cheriton Graduate ScholarshipUNSPECIFIED
Canadian Institute for Advanced Research (CIAR)UNSPECIFIED
Series Name:Lecture Notes in Computer Science
Issue or Number:7582
Record Number:CaltechAUTHORS:20160318-155200133
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65494
Deposited By: Tony Diaz
Deposited On:18 Mar 2016 23:21
Last Modified:10 Nov 2021 23:46

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