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Optimal Counterfeiting Attacks and Generalizations for Wiesner’s Quantum Money

  • Abel Molina
  • Thomas Vidick
  • John Watrous
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7582)

Abstract

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 \((3/4+\sqrt{2}/8)^n\). We also analyze extensions of this variant to higher-dimensional schemes.

Keywords

Dual Problem Success Probability Hermitian Operator Quantum Cloning Counterfeit Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Abel Molina
    • 1
  • Thomas Vidick
    • 2
  • John Watrous
    • 1
  1. 1.Institute for Quantum Computing and School of Computer ScienceUniversity of WaterlooCanada
  2. 2.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyUSA

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