Encoding M classical bits in the relative arrival time of dense-coded photons

We present a scheme to encode M extra classical bits to a dense-coded pair of photons. By tuning the delay of an entangled pair of photons to one of 2 M time-bins and then applying one of the quantum dense coding protocols, a receiver equipped with a synchronized clock of reference is able to decode M bits (via classical time-bin encoding) + 2 bits (via quantum dense coding). This protocol, yet simple, does not dispense several special features of the used programmable delay apparatus to maintain the coherence of the two-photon state. While this type of time-domain encoding may be thought to be ideally of boundless photonic capacity (by increasing the number of available time-bins), errors due to the environmental noise and the imperfect devices and channel evolve with the number of time-bins.