Impossibility of Growing Quantum Bit Commitments

TL;DR

This paper proves that it is impossible to extend quantum bit commitments to longer strings, highlighting fundamental limitations in quantum cryptography.

Contribution

It establishes a theoretical impossibility result showing quantum commitments cannot be grown from a fixed number of bits to longer strings.

Findings

Quantum commitments cannot be extended to longer strings.

Information-theoretic techniques demonstrate fundamental limitations.

No method exists to grow quantum commitments from initial small commitments.

Abstract

Quantum key distribution (QKD) is often, more correctly, called key growing. Given a short key as a seed, QKD enables two parties, connected by an insecure quantum channel, to generate a secret key of arbitrary length. Conversely, no key agreement is possible without access to an initial key. Here, we consider another fundamental cryptographic task, commitments. While, similar to key agreement, commitments cannot be realized from scratch, we ask whether they may be grown. That is, given the ability to commit to a fixed number of bits, is there a way to augment this to commitments to strings of arbitrary length? Using recently developed information-theoretic techniques, we answer this question to the negative.