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Zero knowledge convincing protocol on quantum bit is impossible

Pawel Horodecki·Michal Horodecki·Ryszard Horodecki
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Abstract

Consider two parties: Alice and Bob and suppose 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 Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state $ϕ$ with nonzero probability. This "no-go" result puts general constrains on information processing where information {\it about} quantum state is involved.

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Pawel Horodecki, Michal Horodecki, Ryszard Horodecki. 2017-12-20. Zero knowledge convincing protocol on quantum bit is impossible. https://doi.org/10.22331/q-2017-12-23-41

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