Why quantum state verification cannot be both efficient and secure: a categorical approach

TL;DR

This paper demonstrates a fundamental limitation in quantum state verification, showing that no universal approach can simultaneously achieve both efficiency and security across all quantum states using cut-and-choose methods.

Contribution

The paper introduces a categorical framework to prove a universal trade-off, establishing that existing cut-and-choose verification strategies cannot be both efficient and secure for all quantum states.

Findings

Cut-and-choose techniques cannot be both efficient and secure universally.

A categorical composable cryptography framework is used to establish fundamental limits.

Universal trade-offs exist in quantum state verification protocols.

Abstract

The advantage of quantum protocols lies in the inherent properties of the shared quantum states. These states are sometimes provided by sources that are not trusted, and therefore need to be verified. Finding secure and efficient quantum state verification protocols remains a big challenge, and recent works illustrate trade-offs between efficiency and security for different groups of states in restricted settings. However, whether a universal trade-off exists for all quantum states and all verification strategies remains unknown. In this work, we instantiate the categorical composable cryptography framework to show a fundamental limit for quantum state verification for all cut-and-choose approaches used to verify arbitrary quantum states. Our findings show that the prevailing cut-and-choose techniques cannot lead to quantum state verification protocols that are both efficient and secure.