Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel

Using three-photon polarization-entangled GHZ states or W states, we propose controlled quantum key distribution protocols for circumventing two main types of collective noise, collective dephasing noise, or collective rotation noise. Irrespective of the number of controllers, a three-photon state can generate a one-bit secret key. The storage technique of quantum states is dispensable for the controller and the receiver, and it therefore allows performing the process in a more convenient mode. If the photon cost in a security check is disregarded, then the efficiency theoretically approaches unity.