Knowledge-Concealing Evidencing of Knowledge about a Quantum State
This addresses secure quantum communication for parties needing to verify knowledge without disclosure, but it is incremental as it builds on prior impossibility results.
The paper tackles the problem of proving knowledge about a quantum state without revealing it, showing that zero-knowledge evidencing is impossible in quantum relativistic protocols and no protocol can be both sound and complete. It presents a new protocol conjectured to be near-optimal for large dimensions, with security analysis against attacks.
Bob has a black box that emits a single pure state qudit which is, from his perspective, uniformly distributed. Alice wishes to give Bob evidence that she has knowledge about the emitted state while giving him little or no information about it. We show that zero-knowledge evidencing of such knowledge is impossible in quantum relativistic protocols, extending a previous result of Horodecki et al.. We also show that no such protocol can be both sound and complete. We present a new quantum relativistic protocol which we conjecture to be close to optimal in security against Alice and which reveals little knowledge to Bob, for large dimension $d$. We analyse its security against general attacks by Bob and restricted attacks by Alice.