Why cut-and-choose quantum state verification cannot be both efficient and secure

TL;DR

This paper proves a fundamental limitation showing that cut-and-choose quantum state verification cannot be both efficient and secure, highlighting an inherent trade-off in quantum cryptographic protocols.

Contribution

It establishes a no-go theorem demonstrating the impossibility of achieving both efficiency and security with cut-and-choose quantum state verification methods.

Findings

Cut-and-choose verification cannot be both efficient and secure.

The lower bounds make such protocols effectively unusable.

The result applies to both stand-alone and composable security.

Abstract

Quantum state verification plays a vital role in many quantum cryptographic protocols, as it allows the use of quantum states from untrusted sources. While some progress has been made in this direction, the question of whether the most prevalent type of quantum state verification, namely cut-and-choose verification, can be efficient and secure, is still not answered in full generality. In this work, we show a fundamental limit for quantum state verification for all cut-and-choose approaches used to verify arbitrary quantum states. We provide a no-go result showing that the cut-and-choose techniques cannot lead to quantum state verification protocols that are both efficient in the number of rounds and secure. We show this trade-off for stand-alone and composable security, where the scaling of the lower bound for the security parameters renders cut-and-choose quantum state verification effectively unusable.