Security Analysis for a Class of Quantum Communication Protocols Based on Single-Photon Interferometry

We investigate in detail the assumptions under which secure quantum communications based on a single-photon interferometry scheme can be achieved. A Mach–Zehnder interferometer divided between two parties, with a message carried in the polarization of the photon and the superposition between the arms retained as a monitor for eavesdropping, is an appealing design because it dispenses with complementary bases, discards no photons due to sifting, and appears to offer direct communication without prior key exchange. Indeed, against every adversary who must act on a wavepacket at the moment it passes, the design behaves as intended. A single interaction with one arm is shown to be either informative or invisible but never both, while interception and re-sending is caught on half of the attacked rounds (twice as often as the corresponding attack on BB84 is caught). Moreover, we show that an adversary who detains a wavepacket incurs a delay bounded below by the vacuum traversal time of the link, which for a 50 km separation exceeds detector jitter by six orders of magnitude. However, an adversary equipped with a quantum memory may interact unitarily with the first wavepacket, retain the ancilla without measuring it, and interact with the second when it arrives, recovering the message with certainty while leaving the interference, arrival times, and delivered polarization exactly as they would have been. Notably, this requires neither simultaneous access to the two arms nor any joint operation upon them. The reason is that the message occupies a variable that each wavepacket carries in full, encoded in a public basis, so that a non-demolition measurement of it acts as the identity on the encoded alphabet; moving the message into the relative phase repairs the scheme. We prove that no sequential attack then yields any information whatsoever, and the causal structure of the link (an irrelevance for a locally encoded message) becomes exactly the resource that makes the proof available. We give the resulting security claim, its conditions, and its costs.