Zero knowledge convincing protocol on quantum bit is impossible
arXiv:quant-ph/0010048 · doi:10.22331/q-2017-12-23-41
Abstract
Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $Ï$, unknown to him. Alice knows $Ï$ and she is supposed to convince Bob that she knows $Ï$ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about $Ï$ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state $Ï$ with nonzero probability. This "no-go" result puts general constrains on information processing where information {\it about} quantum state is involved.
4 pages, RevTeX