Earlier quoted context omitted.
That observation of the communication would break the link, versus capture and (attempt to) decrypt?
That to me seems like the coolest possibility. Encryption that breaks if someone other than the authorized parties observes it. Something which isn't possible with "traditional" encryption.
As stated, this isn't possible with encryption enabled by quantum key exchange, either, nor is it an intended goal of the procedure. Quantum key exchange empowers integrity in the cryptographic key exchange process, but it doesn't intrinsically do anything to empower confidentiality (encryption) or authentication. If you successfully share a key with another party using a channel established via quantum entanglement, you will be (theoretically) capable of discerning with certainty whether or not there has been an attempt to record the key "outside" the channel.
The quantum innovation ceases once the key has been successfully shared. The ciphertexts encrypted with a key shared via quantum key exchange are just like ciphertexts encrypted with a key shared via traditional key exchange. They will not "break" if observed by an unauthorized party; in fact, there is no way to endow a ciphertext with that property. Either a party has the correct key or the don't, but the ciphertext will not "self-destruct" or cease to become usable if the incorrect key is used.
I feel this is an important nit to pick because even if you understand this, others reading your comment might not. Conceptually speaking, assurance of secure channel integrity is very different from assurance of confidentiality. It would be more accurate to say that in a quantum channel, you could exchange information in such a way that it cannot feasibly be read or tampered with; however, if the ciphertext were extracted from that channel, it would not be meaningfully different from a ciphertext extracted from TLS.