TY - CHAP
T1 - Optimal counterfeiting attacks and generalizations for Wiesner's quantum money
AU - Molina, Abel
AU - Vidick, Thomas
AU - Watrous, John
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84893344302&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-35656-8_4
DO - 10.1007/978-3-642-35656-8_4
M3 - فصل
SN - 9783642356551
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 45
EP - 64
BT - Theory of Quantum Computation, Communication, and Cryptography - 7th Conference, TQC 2012, Revised Selected Papers
T2 - 7th Conference on Theory of Quantum Computation, Communication, and Cryptography, TQC 2012
Y2 - 17 May 2012 through 19 May 2012
ER -