A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum Entanglement and Communication Complexity
SIAM Journal on Computing
Splitting information securely with entanglement
Information and Computation
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In this paper, we propose new quantum arithmetic protocols among multiple parties. Let some parties have values. A problem is to find a protocol such that under the condition that any eavesdropper intercepting any quantum system being exchanged among the parties must not be able to acquire information, the parties compute an arithmetic operation such as addition and multiplication, and transfer its computing result to another party. One of main ideas to solve this problem is based on operating state phases. A quantum addition algorithm based on operating phases has been proposed by Draper, but his algorithm was not considered being eavesdropped. We propose secure quantum arithmetic protocols.