Abstract
The main purpose of this paper is to prove that (promise) problem Quantum State Identicalness (abbreviated QSI) is essentially complete for perfect zero-knowledge quantum interactive proof (QPZK). Loosely speaking, problem QSI is to decide whether two efficiently preparable quantum states (captured by quantum circuit of polynomial size) are identical or far apart (in trace distance). It is worthy noting that our result does not have classical counterpart yet; natural complete problem for perfect zero-knowledge interactive proof (PZK) is still unknown. Our proof generalizes Watrous’ completeness proof for statistical zero-knowledge quantum interactive proof (QSZK), with an extra idea inspired by Malka to deal with completeness error. With complete problem at our disposal, we can immediately prove (and reprove) several interesting facts about QPZK.
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Yan, J. (2012). Complete Problem for Perfect Zero-Knowledge Quantum Proof. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds) SOFSEM 2012: Theory and Practice of Computer Science. SOFSEM 2012. Lecture Notes in Computer Science, vol 7147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27660-6_34
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