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.
 W. K. Wootters and W. H. Żurek, Nature 299, 802 (1982).
 D. Dieks, Phys. Lett. A 92, 271 (1982).
 H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa and B. Schumacher, Phys. Rev. Lett. 76, 2818 (1996).
 D. Mayers, Phys. Rev. Lett. 78, 3414 (1997).
 H.-K. Lo and H. F. Chau, Phys. Rev. Lett. 78, 3410 (1997).
 A. K. Pati and S. L. Braunstein, Nature 404, 164 (2000).
 N. Gisin and S. Popescu, Phys. Rev. Lett. 83, 432 (1999).
 S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995).
 S. Popescu, Phys. Rev. Lett. 72, 797 (1994).
 R. Horodecki, Phys. Lett. A 187, 145 (1994).
 E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998).
 S. Parker and M. B. Plenio, Phys. Rev. Lett. 85, 3049 (2000).
 Emily Adlam, Adrian Kent, "Knowledge-Concealing Evidencing of Knowledge About a Quantum State", Physical Review Letters 120, 050501 (2018).
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