Zero knowledge convincing protocol on quantum bit is impossible

Abstract

Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $\varphi$, unknown to him. Alice knows $\varphi$ and she is supposed to convince Bob that she knows $\varphi$ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about $\varphi$ 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 $\varphi$ with nonzero probability. This "no-go" result puts general constrains on information processing where information {\it about} quantum state is involved.

4 pages, RevTeX

References in corpus (3)

• On the Power of One Bit of Quantum Information
• Spin flips and quantum information for anti-parallel spins
• Efficient factorization with a single pure qubit and $logN$ mixed qubits

Cited by in corpus (1)

• Knowledge-Concealing Evidencing of Knowledge about a Quantum State