Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $\phi$, unknown to him. Alice knows $\phi$ and she is supposed to convince Bob that she knows $\phi$ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about $\phi$ 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 $\phi$ with nonzero probability. This "no-go" result puts general constrains on information processing where information about quantum state is involved.
 Emily Adlam and Adrian Kent, "Knowledge-Concealing Evidencing of Knowledge About a Quantum State", Physical Review Letters 120 5, 050501 (2018).
 Lewis Westfall and Avery Leider, Advances in Biochemical Engineering/Biotechnology 357 (2020).
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.