Secure quantum string seal exists

Quantum seals are a cryptographic primitive: Alice seals a string of bits into a quantum state, Bob reads it, and any attempt to read it without authorization should be detectable. Perfect seals are impossible, so researchers study imperfect seals that allow a small error rate. In early 2006, Chau posted a proof (quant-ph/0602099) that all quantum string seals are insecure: an eavesdropper could decode the string with non-trivial probability and avoid detection at least half the time.

He responds by rewriting Chau's measurement and computing the probability that a message i' leads to outcome i. With Chau's suggested parameter value, this probability becomes 1/(2N) + λ^2/2, where N is the number of possible messages and λ^2 is a state-dependent amplitude. He then argues that because every message has at least 1/(2N) chance to produce the outcome, there is a probability of 1/2 that the original message is arbitrary, hence the information obtained is zero. This inference is wrong: a lower bound on each likelihood does not imply zero mutual information. The posterior probability of the message still depends on λ^2, so Bob gains some information in every run, not only in half of them.

The paper also proposes a trivial strategy: flip a coin and either read honestly or do nothing. That demonstrates only that partial eavesdropping gives partial information, which is consistent with known bounds. The central rebuttal therefore fails; the insecurity proof stands.