# Knowledge-Concealing Evidencing of Knowledge about a Quantum State

## TL;DR

This paper investigates the limitations and possibilities of quantum relativistic protocols for evidence of knowledge about a quantum state, showing impossibility results and proposing a near-optimal protocol with limited knowledge leakage.

## Contribution

It proves the impossibility of zero-knowledge evidence in quantum relativistic settings and introduces a new protocol that balances security and knowledge concealment.

## Key findings

- Zero-knowledge evidence is impossible in quantum relativistic protocols.
- No protocol can be both sound and complete for this task.
- A new near-optimal protocol is proposed with limited knowledge leakage.

## Abstract

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.