Zero-knowledge convincing protocol on quantum bit is impossible

Paweł Horodecki; Ryszard Horodecki; Michał Horodecki

doi:10.22331/q-2017-12-23-41

Zero-knowledge convincing protocol on quantum bit is impossible

Abstract

It is one of fundamental features of quantum formalism that o n one hand it provides a new infor- mation processing resources and on the other hand puts funda mental constraints on the processing of quantum information implying “no-go” theorems for cloni ng [1–3], bit commitment [4, 5] and deleting [6] in quantum theory. Here we ask about possibilit y of “zero knowledge” scenario which, for its simplicity, can be considered as a quantum primitive or model scenario for any problems of similar kind. Consider two parties: Alice and Bob and suppos e that Bob is given a qubit system in a quantum state φ , unknown to him. Alice knows φ and she is supposed to convince Bob that she knows φ sending some test message. Is it possible for her to convince Bob providing him ”zero knowledge” i. e. no information about φ he has? We prove that there is no ”zero knowledge” protocol of that kind. In fact it turns out that basing on Alic e message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of t he unknown qubit state φ with nonzero probability. This ”no-go” result puts general cons trains on information processing where information about quantum state is involved.

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DOI:: Digital Object Identifier (open in new tab) 10.22331/q-2017-12-23-41
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Category:: Articles
Type:: publikacja w in. zagranicznym czasopiśmie naukowym (tylko język obcy)
Published in:: Quantum Journal no. 1, pages 1 - 41,
ISSN: 2521-327X
Language:: English
Publication year:: 2017
Bibliographic description:: Horodecki P., Horodecki R., Horodecki M.. Zero-knowledge convincing protocol on quantum bit is impossible. Quantum Journal, 2017, Vol. 1, , s.1-41
DOI:: Digital Object Identifier (open in new tab) 10.22331/q-2017-12-23-41
Verified by:: Gdańsk University of Technology