Collective transformations of quantum states with postselection and their application to quantum cryptography

Quantum cryptography allows providing the provable secrecy of distributed cryptographic keys based on fundamental no-go theorems of quantum mechanics. At the same time, some practical limitations of legitimate users can be a potential threat to the security of quantum cryptography protocols. One of the practical difficulties is the use of multiphoton pulses instead of single-photon states. In this paper, we show how the eavesdropper can use multiphoton messages to construct the effective eavesdropping strategy for a quantum cryptography protocol with phase–time coding. This allows obtaining the entire key in the presence of four photons in the pulse instead of five, as was assumed previously. We show that the advantage is achieved due to collective actions with multiphoton messages rather than individual transformations of each photon.